Question
If P, Q, R, S are the points (– 2, 3, 4), (– 4, 4, 6), (4, 3, 5), (0, 1, 2), prove by projection that PQ is perpendicular to RS.
Solution
The given points are P (– 2, 3, 4), Q (– 4, 4, 6), R (4, 3, 5) and S (0, 1, 2).
Direction ratios of RS are. 0 – 4, 1 – 3, 2 – 5 i.e., – 4, – 2, – 3
∴ direction-cosines of RS are
projection of PQ on RS
∴ PQ is perpendicular to RS.
[∵ projection of a line perpendicular to it is zero]
