Question

Show that the line joining the origin to the point(2,1,1)is perpendicular to the line determined by the points(3,5,-1),(4,3,-1).

Answer 1

Let OA be the line joining the origin, O(0,0,0), and the point A(2,1,1).

Also, let BC be the line joining the points B(3,5,-1) and C(4,3,-1).

The direction ratios of OA are 2, 1, and 1 and of BC are (4-3)=1, (3-5)=-2, and (-1+1)=0.

OA is perpendicular to BC, if a₁a₂+b₁b₂+c₁c₂=0

Thus, OA is perpendicular to BC.