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
1
2
3
4
The projection of PQ on x- axis is x2−x1
Hence, the projection of PQon x-axis is d1=3
The projection of PQ on yz-plane is y2−y12+z2−z12
Hence, the projection of PQ on xy- plane is 0−22+−2−02=8=d2
Therefore, d12−d22=9−8=1