First slide
Introduction to 3-D Geometry
Question

Let P=1,2,0,Q=4,0,2 are any two points in the space. Suppose that d1,d2 are the projections of PQ on the x-axis, yz-plane respectively, then d12-d22

Easy
Solution

The projection of PQ on x- axis is x2x1

Hence, the projection of  PQon x-axis is d1=3

The projection of  PQ on yz-plane is y2y12+z2z12

Hence, the projection of PQ on xy- plane is 022+202=8=d2

Therefore, d12d22=98=1

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