Question

The line through the points $(4,7,8),(2,3,4)$ is parallel to the line through the points $(-1,-2,1)$ and $(1,2,5)$.

• A. True
• B. False

Answer 1

The correct option is A True

The line through the points $(4,7,8)$ and $(2,3,4)$ be

$\frac{x-4}{2-4}=\frac{y-7}{3-7}=\frac{z-8}{4-8}$

$\Rightarrow \frac{x-4}{-2}=\frac{y-7}{-4}=\frac{z-8}{-4}$

$\Rightarrow \frac{x-4}{1}=\frac{y-7}{2}=\frac{z-8}{2}$

DR $=<1,2,2>$

The line through the points $(-1,-2,1)$ and $(1,2,5)$ be

$\frac{x-(-1)}{1-(-1)}=\frac{y-(-2)}{2-(-2)}=\frac{z-1}{5-1}$

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

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

DR $=<1,2,2>$

DR of both the lines are same ,

hence they are parallel