Question

If the lines whose cartesian equations are $\frac{x-4}{2}=\frac{y+3}{1}=\frac{z-1}{1}$ and $\frac{x-4}{1}=\frac{y+3}{k}=\frac{z-1}{2}$ are perpendicular to each other, then the value of $k$ is

• A. $-4$
• B. $2$
• C. $-2$
• D. $4$

Answer 1

Answer: (A)

$-4$

Lines are $\frac{x-4}{2}=\frac{y+3}{1}=\frac{z-1}{1}$

and $\frac{x-4}{1}=\frac{y+3}{k}=\frac{z-1}{2}$

$\therefore 2+k+2=0$

$k=-4$