Show that the line segment joining the origin to the point A(2, 1, 1) is perpendicular to the line segment joining the points B(3, 5, -1) and C(4,3, -1).

Question

Philoid · Accepted Answer

Given: O(0, 0, 0) and A(2, 1, 1)

The line joining these two points is given by,

OA = 2i + j +k

B(3, 5, -1) and D(4, 3, -1),

The line joining these two points,

BC = i - 2j +0k

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

So, OA.BC = 0 (dot product)

Thus, (2i + j +k). (i - 2j +0k) = 2 - 2 + 0 = 0.

Thus, the two lines are perpendicular.