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If the image of the point P(1, −2, 3) in the plane, 2x + 3y − 4z + 22 = 0 measured parallel to line, x/1 = y/4 = z/5 is Q, then PQ is equal to:

1. 6√5
2. 3√5
3. 2√42
4. √42

Correct answer: 2√42

Solution

To find the distance PQ, we first determine the projection of point P onto the plane along the given direction. By calculating the intersection of the line defined by P and the direction vector with the plane equation, we find point Q, and then use the distance formula to find PQ, which results in 2√42.

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