The distance of the point $(-1, 9, -16)$ from the plane $2x + 3y - z = 5$ measured parallel to the line $\frac{x+4}{3} = \frac{2-y}{4} = \frac{z-3}{12}$ is:
Step-by-Step Solution
Key Concept: Parametrize the line through the given point with given direction ratios, find intersection with plane, compute distance.
Line through $(-1,9,-16)$ parallel to $(3,-4,12)$: general point $(3\lambda-1, -4\lambda+9, 12\lambda-16)$. Substituting in plane: $6\lambda-2-12\lambda+27-12\lambda+16=5 \Rightarrow \lambda=2$. Point $(5,1,8)$. Distance $= \sqrt{36+64+576} = 26$. Answer: (3)
Correct Answer: 26