Question

The distance of the point $(-1,9,-16)$ from the plane $2 x+3 y-z=5$ measured parallel to the line $\frac{x+4}{3}=\frac{2-y}{4}=\frac{z-3}{12}$ is

• A. $20 \sqrt{2}$
• B. 31
• C. $13 \sqrt{2}$
• D. 26

Answer 1

Answer: (D)

Equation of line
$\frac{x+1}{3}=\frac{y-9}{-4}=\frac{z+16}{12}$
G.P on line $(3 \lambda-1,-4 \lambda+9,12 \lambda-16)$
point of intersection of line \& plane
$6 \lambda-2-12 \lambda+27-12 \lambda+16=5$
$\lambda=2$
Point $(5,1,8)$
Distance $=\sqrt{36+64+576}=26$