Find the value of p for which the line through the points A(3, 5, -1) and B(5, p, 0) 9 is perpendicular to the line through the points C(2, 1, 1) and D (3, 3, -1).

Question

Philoid · Accepted Answer

Given: A(3, 5, -1) and B(5, p, 0)

The line joining these two points is given by,

AB = 2i + (p-5)j + k

C(2, 1, 1) and D(3, 3, -1),

The line joining these two points,

CD = i + 2j - 2k

As the two lines are perpendicular, we know that the angle between these two lines is

So, AB.CD = 0 (dot product)

Thus, (2i + (p-5)j + k) .(i + 2j - 2k) = 0.

ð

ð p = 5

Thus, p = 5.