Question

The equation of line passing through point $A(2,-1,1)$ and parallel to vector $2\hat{i}+3\hat{j}-\hat{k}$ is

• A. $\frac{x+2}{2}=\frac{y-1}{3}=\frac{z-1}{-1}$
• B. $\frac{x+2}{-2}=\frac{y+1}{-1}=\frac{z-1}{-1}$
• C. $\frac{x-2}{2}=\frac{y+1}{3}=\frac{z-1}{-1}$
• D. $\frac{x-2}{2}=\frac{y-1}{3}=\frac{z-1}{-1}$

Answer 1

The correct option is C $\frac{x-2}{2}=\frac{y+1}{3}=\frac{z-1}{-1}$

Equation of line passing through point $A(x_1,y_1,z_1)$ and parallel to vector $\overrightarrow{B}=a\hat{i}+b\hat{j}+c\hat{k}$ is given by :
$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$
Given : $(a,b,c)=(2,3,-1)$ and $(x_1,y_1,z_1)=(2,-1,1)$
So, equation of line is given by
$\frac{x-2}{2}=\frac{y+1}{3}=\frac{z-1}{-1}$