Question

Equation of the line passing through the point $(2,3,1)$ and parallel to the line of the intersection of the plane $x-2y-z+5=0\text{and}x+y+3z=6$ is

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

Answer 1

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

Direction vector of the line of intersection of the planes is
$\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& -2& -1\\ 1& 1& 3\end{array}\right|=-5\hat{i}-4\hat{j}+3\hat{k}\therefore \text{The equation of line is}\frac{x-2}{-5}=\frac{y-3}{-4}=\frac{z-1}{3}$