Diketahui vektor a ‾ = i ‾ − j ‾ + k ‾ \overline{a}=\overline{i}-\overline{j}+\overline{k} a = i − j + k , b ‾ = i ‾ + j ‾ + 2 k ‾ \overline{b}=\overline{i}+\overline{j}+2\overline{k} b = i + j + 2 k , dan c ‾ = 3 i ‾ − k ‾ \overline{c}=3\overline{i}-\overline{k} c = 3 i − k . Panjang proyeksi ( b ‾ + c ‾ ) \left(\overline{b}\ +\overline{c}\right) ( b + c ) pada a ‾ \overline{a} a adalah ...

1 1 3 3 1\frac{1}{3}\sqrt{3} 1 3 1 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

3 2 2 \frac{3}{2}\sqrt{2} 2 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 2 2\sqrt{2} 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

4 3 4\sqrt{3} 4 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 3 3 \frac{2}{3}\sqrt{3} 3 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Diketahui segitiga ABC dengan titik A(-2,3,1), B(3,-1,2) dan C(2,1,-3). Jika u ‾ \overline{u} u mewakili A B ‾ \overline{AB} A B dan v ‾ \overline{v} v mewakili A C ‾ \overline{AC} A C , maka vektor proyeksi u ‾ p a d a v ‾ \overline{u}\ pada\ \overline{v} u p a d a v adalah...

8 3 i ‾ − 4 3 j ‾ − 8 3 k ‾ \frac{8}{3}\overline{i}-\frac{4}{3}\overline{j}-\frac{8}{3}\overline{k} 3 8 i − 3 4 j − 3 8 k

− 3 2 i ‾ + 2 j ‾ − 1 2 k ‾ -\frac{3}{2}\overline{i}+2\overline{j}-\frac{1}{2}\overline{k} − 2 3 i + 2 j − 2 1 k

3 2 i ‾ − 2 j ‾ + 1 2 k ‾ \frac{3}{2}\overline{i}-2\overline{j}+\frac{1}{2}\overline{k} 2 3 i − 2 j + 2 1 k

− 8 3 i ‾ + 4 3 j ‾ + 8 3 k ‾ -\frac{8}{3}\overline{i}+\frac{4}{3}\overline{j}+\frac{8}{3}\overline{k} − 3 8 i + 3 4 j + 3 8 k

4 3 i ‾ − 2 3 j ‾ − 4 3 k ‾ \frac{4}{3}\overline{i}-\frac{2}{3}\overline{j}-\frac{4}{3}\overline{k} 3 4 i − 3 2 j − 3 4 k

Diketahui vektor a ‾ = i ‾ − 2 j ‾ − 2 k ‾ \overline{a}=\overline{i}-2\overline{j}-2\overline{k} a = i − 2 j − 2 k dan vektor b ‾ = 5 i ‾ + 6 j ‾ + k ‾ \overline{b}=5\overline{i}+6\overline{j}+\overline{k} b = 5 i + 6 j + k . Proyeksi ortogonal vektor b ‾ p a d a a ‾ \overline{b}\ pada\ \overline{a} b p a d a a adalah...

− i ‾ + 2 j ‾ + 2 k ‾ -\overline{i}+2\overline{j}+2\overline{k} − i + 2 j + 2 k

i ‾ + 2 j ‾ + 2 k ‾ \overline{i}+2\overline{j}+2\overline{k} i + 2 j + 2 k

i ‾ + 2 j ‾ − 2 k ‾ \overline{i}+2\overline{j}-2\overline{k} i + 2 j − 2 k

i ‾ − 2 j ‾ + 2 k ‾ \overline{i}-2\overline{j}+2\overline{k} i − 2 j + 2 k

2 i ‾ + 2 j ‾ − k ‾ 2\overline{i}+2\overline{j}-\overline{k} 2 i + 2 j − k

Diketahui m ‾ = 6 i ‾ − 2 j ‾ − 4 k ‾ \overline{m}=6\overline{i}-2\overline{j}-4\overline{k} m = 6 i − 2 j − 4 k dan n ‾ = 2 i ‾ + j ‾ − 2 k ‾ \overline{n}=2\overline{i}+\overline{j}-2\overline{k} n = 2 i + j − 2 k . Proyeksi vektor ortogonal m ‾ p a d a n ‾ \overline{m}\ pada\ \overline{n} m p a d a n adalah...

4 i ‾ + 2 j ‾ − 4 k ‾ 4\overline{i}+2\overline{j}-4\overline{k} 4 i + 2 j − 4 k

2 i ‾ + j ‾ − 4 k ‾ 2\overline{i}+\overline{j}-4\overline{k} 2 i + j − 4 k

i ‾ + 1 2 j ‾ − k ‾ \overline{i}+\frac{1}{2}\overline{j}-\overline{k} i + 2 1 j − k

2 3 i ‾ + 1 3 j ‾ − 2 3 k ‾ \frac{2}{3}\overline{i}+\frac{1}{3}\overline{j}-\frac{2}{3}\overline{k} 3 2 i + 3 1 j − 3 2 k

6 i ‾ + 3 j ‾ − 6 k ‾ 6\overline{i}+3\overline{j}-6\overline{k} 6 i + 3 j − 6 k

Diketahui vektor-vektor u ‾ = b i ‾ − 12 j ‾ + a k ‾ \overline{u}=b\overline{i}-12\overline{j}+a\overline{k} u = b i − 1 2 j + a k dan v ‾ = a i ‾ + a j ‾ − b k ‾ \overline{v}=a\overline{i}+a\overline{j}-b\overline{k} v = a i + a j − b k . Sudut antara vektor u ‾ d a n v ‾ \overline{u}\ dan\ \overline{v} u d a n v adalah θ \theta θ dengan cos ⁡ θ = 3 4 \cos\ \theta\ =\frac{\sqrt{3}}{4} cos θ = 4 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> . Proyeksi vektor u ‾ p a d a v ‾ \overline{u}\ pada\ \overline{v} u p a d a v adalah p ‾ = − 4 i ‾ − 4 j ‾ + 4 k ‾ \overline{p}=-4\overline{i}-4\overline{j}+4\overline{k} p = − 4 i − 4 j + 4 k . Nilai dari b =...

2 14 2\sqrt{14} 2 1 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

4 7 4\sqrt{7} 4 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 7 2\sqrt{7} 2 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

14 \sqrt{14} 1 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

7 \sqrt{7} 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Diketahui vektor a ‾ = 3 i ‾ − 2 j ‾ + 4 k ‾ \overline{a}=3\overline{i}-2\overline{j}+4\overline{k} a = 3 i − 2 j + 4 k dan vektor b ‾ = − i ‾ + j ‾ + 2 k ‾ \overline{b}=-\overline{i}+\overline{j}+2\overline{k} b = − i + j + 2 k . Proyeksi vektor ortogonal a ‾ \overline{a} a pada vektor b ‾ \overline{b} b adalah...

1 2 ( − i ‾ + j ‾ + 2 k ‾ ) \frac{1}{2}\left(-\overline{i}+\overline{j}+2\overline{k}\right) 2 1 ( − i + j + 2 k )

1 6 ( − i ‾ + j ‾ + 2 k ‾ ) \frac{1}{6}\left(-\overline{i}+\overline{j}+2\overline{k}\right) 6 1 ( − i + j + 2 k )

1 3 ( − i ‾ + j ‾ + 2 k ‾ ) \frac{1}{3}\left(-\overline{i}+\overline{j}+2\overline{k}\right) 3 1 ( − i + j + 2 k )

− i ‾ + j ‾ + 2 k ‾ -\overline{i}+\overline{j}+2\overline{k} − i + j + 2 k

− 2 i ‾ + 2 j ‾ + 4 k ‾ -2\overline{i}+2\overline{j}+4\overline{k} − 2 i + 2 j + 4 k

Panjang proyeksi vektor a ‾ = 2 i ‾ + y j ‾ + k ‾ \overline{a}=2\overline{i}+y\overline{j}+\overline{k} a = 2 i + y j + k pada b ‾ = 2 i ‾ + 2 j ‾ + k ‾ \overline{b}=2\overline{i}+2\overline{j}+\overline{k} b = 2 i + 2 j + k sama dengan setengah kali panjang vektor b ‾ \overline{b} b . Dengan demikian vektor proyeksi vektor b ‾ \overline{b} b pada a ‾ \overline{a} a adalah...

16 9 i ‾ − 2 9 j ‾ + 8 9 k ‾ \frac{16}{9}\overline{i}-\frac{2}{9}\overline{j}+\frac{8}{9}\overline{k} 9 1 6 i − 9 2 j + 9 8 k

2 i ‾ + 2 j ‾ + k ‾ 2\overline{i}+2\overline{j}+\overline{k} 2 i + 2 j + k

1 2 i ‾ + 1 2 j ‾ + 1 4 k ‾ \frac{1}{2}\overline{i}+\frac{1}{2}\overline{j}+\frac{1}{4}\overline{k} 2 1 i + 2 1 j + 4 1 k

i ‾ + j ‾ + 1 2 k ‾ \overline{i}+\overline{j}+\frac{1}{2}\overline{k} i + j + 2 1 k

1 3 i ‾ + 1 3 j ‾ + 1 6 k ‾ \frac{1}{3}\overline{i}+\frac{1}{3}\overline{j}+\frac{1}{6}\overline{k} 3 1 i + 3 1 j + 6 1 k

Diketahui vektor a ‾ = i ‾ + 2 j ‾ + x k ‾ \overline{a}=\overline{i}+2\overline{j}+x\overline{k} a = i + 2 j + x k dan vektor b ‾ = 2 i ‾ + j ‾ − k ‾ \overline{b}=2\overline{i}+\overline{j}-\overline{k} b = 2 i + j − k serta panjang proyeksi vektor a ‾ \overline{a}\ a pada vektor b ‾ \overline{b} b adalah 1 3 6 \frac{1}{3}\sqrt{6} 3 1 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> . Sudut antara vektor \overline{a}\ a dan vektor \overline{b} b adalah α \alpha α , maka cos ⁡ α \cos\ \alpha cos α =...

1 9 6 \frac{1}{9}\sqrt{6} 9 1 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

1 6 6 \frac{\text{1}}{\text{6}}\sqrt{6} 6 1 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

3 6 6 \frac{\text{3}}{\text{6}}\sqrt{6} 6 3 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 9 6 \frac{2}{9}\sqrt{6} 9 2 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

1 3 6 \frac{1}{3}\sqrt{6} 3 1 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Quiz Proyeksi Vektor

Authored by Siti Khoiriyah

Mathematics

1st Grade

Used 37+ times

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20 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$Diketahui\ u⃗=2i+j-2k\ dan$
$v⃗=i+3j+k.Tentukan\ panjang\$
$proyeksi\ orthogonal\ u⃗\ pada\ v⃗.$

$1/√11$

$2/√11$

$3/√11$

$4/√11$

$5/√11$

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Jika vektor a = xi - 4j + 8k tegak lurus vektor b = 2xi + 2xj - 3k, maka nilai x yang memenuhi adalah

-2 atau 6

-3 atau 4

-4 atau 3

-6 atau 2

-2 atau - 3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Diketahui p = 6i + 7j - 6k dan
q = xi + j + 4k. Jika panjang proyeksi q pada p adalah 2, maka x adalah

5/6

3/2

13/2

43/6

53/6

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$Diketahui\ u⃗=2i+j-2k\ dan$
$v⃗=i+3j+k.Tentukan\ panjang\$
$proyeksi\ orthogonal\ u⃗\ pada\ v⃗.$

$1/√11$

$2/√11$

$3/√11$

$4/√11$

$5/√11$

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Jika vektor a = –3i – j + xk dan vektor
b = 3i – 2j + 6k. Jika panjang proyeksi vektor a pada b adalah 5, maka nilai x = …

-7

-6

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Diketahui titik-titik A (3,-1,0), B(2,4,1) dan C(1.0,5). Maka panjang proyeksi vektor AB pada vektor BC adalah...
A. 1/5 √30
B. 2/5 √30
C. 3/5 √30
D. 4/5 √30
E. √30

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$\overline{A}\ =\ mi+4j+2k$

$\overline{B}=-7i+mj+6k$

Vektor A tegak lurus dengan Vektor B
Tentukan nilai m

A. 4

B. 2

C. -7

D. 6

E. 1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Diketahui vektor $\overline{a}=2\overline{i}-2\overline{j}+x\overline{k}$ dan vektor $\overline{b}=-3\overline{i}-4\overline{j}+12\overline{k}$ . Jika panjang proyeksi vektor $\overline{a}\$ pada vektor $\overline{b}$ adalah 2, maka nilai x sama dengan....

-2

-1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Diketahui segitiga ABC dengan titik A(-2,3,1), B(3,-1,2) dan C(2,1,-3). Jika $\overline{u}$ mewakili $\overline{AB}$ dan $\overline{v}$ mewakili $\overline{AC}$ , maka proyeksi skalar $\overline{u}\ pada\ \overline{v}$ adalah...

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Diketahui vektor $\overline{a}=\overline{i}-\overline{j}+\overline{k}$ , $\overline{b}=\overline{i}+\overline{j}+2\overline{k}$ , dan $\overline{c}=3\overline{i}-\overline{k}$ . Panjang proyeksi $\left(\overline{b}\ +\overline{c}\right)$ pada $\overline{a}$ adalah ...

$\frac{3}{2}\sqrt{2}$

$2\sqrt{2}$

$4\sqrt{3}$

$1\frac{1}{3}\sqrt{3}$

$\frac{2}{3}\sqrt{3}$

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Quiz Proyeksi Vektor

Diketahui u⃗=2i+j−2k danDiketahui\ u⃗=2i+j-2k\ danDiketahui u⃗=2i+j−2k dan v⃗=i+3j+k.Tentukan panjang v⃗=i+3j+k.Tentukan\ panjang\ v⃗=i+3j+k.Tentukan panjang proyeksi orthogonal u⃗ pada v⃗.proyeksi\ orthogonal\ u⃗\ pada\ v⃗.proyeksi orthogonal u⃗ pada v⃗.

Jika vektor a = xi - 4j + 8k tegak lurus vektor b = 2xi + 2xj - 3k, maka nilai x yang memenuhi adalah

Diketahui p = 6i + 7j - 6k danq = xi + j + 4k. Jika panjang proyeksi q pada p adalah 2, maka x adalah

Diketahui u⃗=2i+j−2k danDiketahui\ u⃗=2i+j-2k\ danDiketahui u⃗=2i+j−2k dan v⃗=i+3j+k.Tentukan panjang v⃗=i+3j+k.Tentukan\ panjang\ v⃗=i+3j+k.Tentukan panjang proyeksi orthogonal u⃗ pada v⃗.proyeksi\ orthogonal\ u⃗\ pada\ v⃗.proyeksi orthogonal u⃗ pada v⃗.

Jika vektor a = –3i – j + xk dan vektorb = 3i – 2j + 6k. Jika panjang proyeksi vektor a pada b adalah 5, maka nilai x = …

Diketahui titik-titik A (3,-1,0), B(2,4,1) dan C(1.0,5). Maka panjang proyeksi vektor AB pada vektor BC adalah...A. 1/5 √30B. 2/5 √30C. 3/5 √30D. 4/5 √30 E. √30

A‾ = mi+4j+2k\overline{A}\ =\ mi+4j+2kA = mi+4j+2k B‾=−7i+mj+6k\overline{B}=-7i+mj+6kB=−7i+mj+6k Vektor A tegak lurus dengan Vektor BTentukan nilai m

Diketahui segitiga ABC dengan titik A(-2,3,1), B(3,-1,2) dan C(2,1,-3). Jika u‾\overline{u}u mewakili AB‾\overline{AB}AB dan v‾\overline{v}v mewakili AC‾\overline{AC}AC , maka proyeksi skalar u‾ pada v‾\overline{u}\ pada\ \overline{v}u pada v adalah...

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$Diketahui\ u⃗=2i+j-2k\ dan$
$v⃗=i+3j+k.Tentukan\ panjang\$
$proyeksi\ orthogonal\ u⃗\ pada\ v⃗.$

Diketahui p = 6i + 7j - 6k dan
q = xi + j + 4k. Jika panjang proyeksi q pada p adalah 2, maka x adalah

$Diketahui\ u⃗=2i+j-2k\ dan$
$v⃗=i+3j+k.Tentukan\ panjang\$
$proyeksi\ orthogonal\ u⃗\ pada\ v⃗.$

Jika vektor a = –3i – j + xk dan vektor
b = 3i – 2j + 6k. Jika panjang proyeksi vektor a pada b adalah 5, maka nilai x = …

Diketahui titik-titik A (3,-1,0), B(2,4,1) dan C(1.0,5). Maka panjang proyeksi vektor AB pada vektor BC adalah...
A. 1/5 √30
B. 2/5 √30
C. 3/5 √30
D. 4/5 √30
E. √30

$\overline{A}\ =\ mi+4j+2k$

$\overline{B}=-7i+mj+6k$

Vektor A tegak lurus dengan Vektor B
Tentukan nilai m

Diketahui segitiga ABC dengan titik A(-2,3,1), B(3,-1,2) dan C(2,1,-3). Jika $\overline{u}$ mewakili $\overline{AB}$ dan $\overline{v}$ mewakili $\overline{AC}$ , maka proyeksi skalar $\overline{u}\ pada\ \overline{v}$ adalah...