Quiz about Perbandingan, panjang, jarak pada vektor dan vektor satuan

Question 1

Diketahui koordinat titik M(2, -4) dan N(8, 5). Jika $$\overrightarrow{MP}\ :\ \overrightarrow{PN}$$ = 1 : 2, koordinat titik P adalah ... .

Accepted Answer

(4, -1)

Answer

(4, 2)

Answer

(4, 1)

Answer

(6, 2)

Answer

(6, -2)

Question 2

Koordinat titik tengah K(1, -3, 2) dan L(-3, -1, 8) adalah ... .

Accepted Answer

(-1, -2, 5)

Answer

(1, -1, 5)

Answer

(1, -1, 5)

Answer

(1, -2, 5)

Answer

(-1, 2, 5)

Question 3

Diketahui koordinat titik A(1, -1, 4) dan B(-1, 3, -2). Jika $$\overrightarrow{AB}\ :\ \overrightarrow{BC}$$ = 2 : 1, koordinat titik C adalah ... .

Accepted Answer

(-2, 5, -5)

Answer

( $$\frac{1}{3},\frac{5}{3},\ 2$$ )

Answer

( $$-\frac{1}{3},\ \frac{5}{3},\ 0$$ )

Answer

(2, 5, -5)

Answer

(-2, -5, 5)

Question 4

Diketahui $$\overrightarrow{v}$$ = $$\overrightarrow{a}+\overrightarrow{b}$$ , jika $$\overrightarrow{a}$$ = (1, 3) dan $$\overrightarrow{b}$$ = (-3, 1), panjang $$\overrightarrow{v}$$ adalah ... .

Accepted Answer

2 $$\sqrt[]{5}$$

Answer

$$\sqrt[]{5}$$

Answer

$$\sqrt[]{10}$$

Answer

4 $$\sqrt[]{5}$$

Answer

3 $$\sqrt[]{15}$$

Question 5

Jika $$\overrightarrow{p}=\overrightarrow{i}-2\overrightarrow{j}-7\overrightarrow{k}$$ , panjang vektor $$\overrightarrow{p}$$ adalah $$\left|\overrightarrow{p}\right|$$ = ... .

Accepted Answer

3 $$\sqrt[]{6}$$

Answer

6 $$\sqrt[]{3}$$

Answer

9 $$\sqrt[]{6}$$

Answer

27

Answer

54

Question 6

Jika titik C memiliki koordinat (1, 5) dan titik D memiliki koordinat (4, 8), jarak antara kedua titik tersebut adalah ... .

Accepted Answer

3 $$\sqrt[]{2}$$

Answer

7 $$\sqrt[]{2}$$

Answer

10 $$\sqrt[]{2}$$

Answer

5 $$\sqrt[]{2}$$

Answer

2 $$\sqrt[]{2}$$

Question 7

Jika titik G memiliki koordinat (5, 6) dan titik H memiliki koordinat (5, 10), jarak antara kedua titik tersebut adalah ... .

Accepted Answer

4

Answer

2

Answer

1

Answer

10

Answer

5

Question 8

Berikut yang merupakan vektor satuan adalah ... .

Accepted Answer

( $$\frac{1}{3},\frac{2}{3},-\frac{2}{3}$$ )

Answer

( $$-\frac{1}{\sqrt[]{3}},\frac{2}{\sqrt[]{3}},\frac{2}{\sqrt[]{3}}$$ )

Answer

(-1, 2, 2)

Answer

(0, 2, 5)

Answer

( $$\frac{1}{5},\frac{2}{5},\frac{2}{5}$$ )

Question 9

Vektor satuan yang searah dengan $$\overrightarrow{u}$$ = (1, 2) adalah ... .

Accepted Answer

( $$\frac{1}{\sqrt[]{5}},\ \frac{2}{\sqrt[]{5}}$$ )

Answer

(1, 2)

Answer

(2, 1)

Answer

( $$\frac{1}{5},\frac{2}{5}$$ )

Answer

$$\frac{1}{\sqrt[]{3}},\frac{2}{\sqrt[]{3}}$$

Question 10

Diketahui koordinat titik P(0, 3, 2) dan Q(3, 6, -1). Vektor satuan searah dari $$\overrightarrow{PQ}$$ adalah ... .

Accepted Answer

$$\frac{1}{\sqrt[]{3}}\left(\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k}\right)$$

Answer

$$\frac{1}{\sqrt[]{3}}\left(-\overrightarrow{i}-\overrightarrow{j}+\overrightarrow{k}\right)$$

Answer

$$\frac{1}{\sqrt[]{3}}\left(-\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}\right)$$

Answer

$$\frac{1}{\sqrt[]{3}}\left(\overrightarrow{i}-\overrightarrow{j}+\overrightarrow{k}\right)$$

Answer

$$\frac{1}{\sqrt[]{3}}\left(\overrightarrow{i}-\overrightarrow{j}-\overrightarrow{k}\right)$$

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