MathLabs

Problem 4

Given a plane π\pi, a point PP in π\pi and a point QQ not in π\pi, find all points RR in π\pi such that the ratio QP+PRQR\dfrac{QP+PR}{QR} is a maximum.
Step 1 of 5: Project Q onto the plane
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X=foot of the perpendicular from Q to πX=\text{foot of the perpendicular from }Q\text{ to }\pi
Detailed analysis

Let X be the foot of the perpendicular from Q to π. It is the point of π closest to Q and will determine the direction of the maximizing point.