ILL 1990 Problem 43

Let $V$ be a finite set of points in three-dimensional space. Let $S_1, S_2, S_3$ be the sets consisting of the orthogonal projections of the points of $V$ onto the $yz$ -plane, $zx$ -plane, $xy$ -plane, respectively. Prove that $| V|^2 \leq | S1|\cdot|S2|\cdot |S3|$ , where $| A|$ denotes the number of elements in the finite set $A.$