Question

The equation of a line passing through the point $(4,-2,5)$ and parallel to the vector $3\hat{i}-\hat{j}+2\hat{k}$ in Cartesian form is

• A. $\frac{x-4}{3}=\frac{y+2}{-1}=\frac{z-5}{2}$
• B. $\frac{x+4}{3}=\frac{y-2}{-1}=\frac{z+5}{2}$
• C. $\frac{x-4}{-3}=\frac{y+2}{-1}=\frac{z-5}{-2}$
• D. $\frac{x-4}{-3}=\frac{y-2}{-1}=\frac{z-5}{2}$

Answer 1

The correct option is A $\frac{x-4}{3}=\frac{y+2}{-1}=\frac{z-5}{2}$

Vector equation of line is : $\overrightarrow{r}=(4\hat{i}-2\hat{j}+5\hat{k})+\lambda (3\hat{i}-\hat{j}+2\hat{k})$
$\Rightarrow x=4+3\lambda ,y=-2-\lambda ,z=5+2\lambda$
eliminating $\lambda$ from above equation,
$\Rightarrow \frac{x-4}{3}=\frac{y+2}{-1}=\frac{z-5}{2}$