Answer to Question #86810 in Calculus for Swati malik

Question

A, B, C, D, are the points i - k, -i + 2j, 2i - 3k, 3i - 2j - k respectively. Show that the projection of AB on CD is equal to that of CD on AB. Also find the cosine of their inclination.

Answer 1

AB = [-2, 2, 1] or -2i + 2j + k

CD = [1, -2, 2] or i - 2j + 2k

AB*CD = (-2)*1 + 2*(-2) + 1*2 = -4

|AB| = sqrt((-2)^2 + 2^2 + 1^2) = sqrt(9) = 3

|CD| = sqrt(1^1 + (-2)^2 + 2^2) = sqrt(9) = 3

Projecton of AB on CD = AB*CD/|CD| = -4/3

Projecton of CD on AB = AB*CD/|AB| = -4/3

cosine of inclination = AB*CD/(|AB|*|CD|) = -4/9