Question

The equation of line passing through the point $(2,1,-1)$ and parallel to the line $\frac{x-3}{1}=\frac{y-2}{-1}=\frac{z+1}{2}$ is

[2 marks]

• A. $\frac{x+2}{1}=\frac{y+1}{-1}=\frac{z-1}{2}$
• B. $\frac{x-2}{1}=\frac{y-1}{-1}=\frac{z+1}{-2}$
• C. $\frac{x+2}{1}=\frac{y-1}{1}=\frac{z+1}{2}$
• D. $\frac{x-2}{1}=\frac{y-1}{-1}=\frac{z+1}{2}$

Answer 1

The correct option is D $\frac{x-2}{1}=\frac{y-1}{-1}=\frac{z+1}{2}$

Given line, $\frac{x-3}{1}=\frac{y-2}{-1}=\frac{z+1}{2}$
The direction ratios of the given line are $1,-1,2$

We know that parallel lines have same direction ratios.
$\therefore$ Equation of line passing through the point $(2,1,-1)$ and having direction ratios $1,-1,2$ is
$\frac{x-2}{1}=\frac{y-1}{-1}=\frac{z+1}{2}$