Question

Задача 4 на фото решить пункт 1,2,3
Вариант 20
Очень нужно

Answer 1

$A_1(7;7;8)\ ,\ A_2(6;6;8)\ ,\ A_3(8;5;8)\ ,\ A_4(8;1;1)\\\\\\1)\ \ \overline{A_1A_2}=(-1;-1;0)\\\\|\overline{A_1A_2}|=\sqrt{(-1)^2+(-1)^2+0^2}=\sqrt2\\\\\\2)\ \ A_1A_2:\ \ \dfrac{x-7}{-1}=\dfrac{y-7}{-1}=\dfrac{z-8}{[0]}\ \ \ ili\ \ \ \ \left\{\begin{array}{l}x=7-t\\y=7-t\\z=8\end{array}\right$

$3)\ \ \overline{A_1A_4}=(1;-6;-7)\\\\cos\angle (\overline{A_1A_2}\ ,\, \overline{A_1A_4})=\dfrac{\overline{A_1A_2}\, \cdot \, \overline{A_1A_4}}{|\overline{A_1A_2}|\, \cdot \, |\overline{A_1A_4}|}=\dfrac{1+6+0}{\sqrt2\cdot \sqrt{1^2+(-6)^2+(-7)^2}}=\\\\\\=\dfrac{7}{\sqrt2\cdot \sqrt{86}}=\dfrac{7}{\sqrt{172}}\\\\\\\angle (\overline{A_1A_2}\ ,\, \overline{A_1A_4})=arccos\dfrac{7}{\sqrt{172}}$