Show that the line joining the points A(1,-1, 2) and B(3, 4, -2) is perpendicular to the line joining the points C(0, 3, 2) and D (3, 5, 6).

Question

Philoid · Accepted Answer

Given: A(1, -1, 2) and B(3, 4, -2)

The line joining these two points is given by,

AB = 2i + 5j -4k

C(0, 3, 2) and D(3, 5, 6),

The line joining these two points,

CD = 3i + 2j +4k

To prove that the two lines are perpendicular we need to show that the angle between these two lines is

So, AB.CD = 0 (dot product)

Thus, (2i + 5j -4k). (3i + 2j +4k) = 6 + 10 – 16 = 0.

Thus, the two lines are perpendicular.