Question

The line through the points $(1,-1,2),(3,4,-2)$ is perpendicular to the line through the points $(0,3,2)$ and $(3,5,6)$.

• A. True
• B. False

Answer 1

The correct option is A True

The line through points $(1,-1,2)$ and $(3,4,-2)$

$\frac{x-1}{3-1}=\frac{y-(-1)}{4-(-1)}=\frac{z-2}{-2-2}$

$\Rightarrow \frac{x-1}{2}=\frac{y+1}{5}=\frac{z-2}{-4}$

DR of the line $=<2,5,-4>$

The line through point $(0,3,2)$and $(3,5,6)$

$\frac{x-0}{3-0}=\frac{y-3}{5-3}=\frac{z-2}{6-2}$

$\Rightarrow \frac{x}{3}=\frac{y-3}{2}=\frac{z-2}{4}$

DR of the line $=<3,2,4>$

$\therefore$ For $\perp$,

$a_1{a}_2+b_1{b}_2+c_1{c}_2=0$

$\Rightarrow 3\left(2\right)+\left(2\right)5+4(-4)$

$\Rightarrow 6+10+-16$

$=0$ Hence they are perpendicular to each other