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

Dr’s of the line joining the origin to the point (2,1,1 )is (2 – 0, 1 – 0, 1 – 0) 

∴ (2, 1,1) 

Dr’s of the line joining (3, 5,-1) and (+4, 3,-1) is (4 – 3 ,3 – 5,1 – 1) (1, -2, 0) 

1 x 2 – 2 x 1 + 1 x 0 = 0 

hence a₁b₁ + a₂b₂ + a₃b₃ = 0 

∴ lines are perpendicular.