$$\left(x_1;y_1\right)\ және\ \left(x_2;y_2\right)нүктелерінің\ арақашықтығы$$

$$d=\sqrt[]{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$$

$$\left(x_1;y_1;z_1\right)және\ \left(x_2;y_2;z_2\right)нүктелерінің\ арақашықтығы$$

$$d=\sqrt[]{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}$$

Векторлардың тең болу шарты

𝑎⃗ = 𝑏⃗ $$\Longleftrightarrow a_1=a_2;b_1=b_2$$

$$a^{\longrightarrow}\left(a_1;a_2\right)\ және\ b^{\rightarrow}\left(b_1;b_2\right)векторларының\ коллинеарлық\ шарты$$

$$\frac{a_1}{b_1}=\frac{a_2}{b_2}=\lambda$$

𝑎⃗ және 𝑏⃗ векторының скаляр көбейтіндісі

𝑎⃗ ∙ 𝑏⃗= $$\left|a^{\rightarrow}\right|\cdot\left|b^{\rightarrow}\right|\cos\alpha$$

Скаляр көбейтудің қасиеттері

1. 𝑎⃗ ∙ 𝑎⃗ = $$a^{\rightarrow^2}$$ 2.𝑎⃗ ∙ 𝑏⃗ = 𝑏⃗ $$\cdot a^{\rightarrow}$$ 3. (𝑎⃗ ∙ 𝑏⃗) ∙ 𝑐⃗ = 𝑎⃗ ∙ (𝑏⃗ ∙ 𝑐⃗) 4. (𝑚𝑎⃗) ∙ (𝑛𝑏⃗) = 𝑚𝑛 ∙ (𝑎⃗ ∙ 𝑏⃗)

Координат векторлар

$$i^{\rightarrow}=\left(1;0;0\right)\ j^{\rightarrow}=\left(0;1;0\right)\ k^{\rightarrow}=\left(0;0;1\right)$$

Аналитикалық геометрия элементтері; вектор Flashcards

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АВ кесіндісінің ортасы болатын С нүктесінің координаталары

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(𝑥; 𝑦; 𝑧) нүктесінен бас нүктеге дейінгі арақашықтық

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АВ кестесінің ортасы болатын М нүктесінің координаталары

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