Question

The distance of the point \( (1, -2, 3) \) from the plane \( x - y + z = 5 \) measured parallel to the line \[ \frac{x}{2} = \frac{y}{3} = \frac{z - 1}{6} \] is

• A. \( \frac{3}{2} \)
• B. 3
• C. \( \sqrt{5} \)
• D. 4

Hint:

For finding the distance from a point to a plane in a given direction, use the projection of the point onto the plane.

Answer 1

The Correct Option is C

The distance from a point to a plane in the direction of a line can be computed by projection. First, express the line's direction ratios and then use the projection formula.
Final Answer: \[ \boxed{\sqrt{5}} \]