Question

If A(1, 2, 3) and B(4, 5, 6) are two points, then find the foot of the perpendicular from the point B to the line joining the origin and point A.

Answer 1

Let M be the foot of the perpendicular drawn from B to the line joining O and A.

Let M = (x, y, z) 

OM has direction ratios x – 0, y – 0, z – 0 = x, y, z 

OA has direction ratios 1 – 0, 2 – 0, 3 – 0 = 1, 2, 3 

But O, M, A are collinear.

∵ BM has direction ratios

k – 4, 2k – 5, 3k – 6

BM is perpendicular to OA