Consider the following xy5z 0 5xy420 a Find the angle betwee

Consider the following. x+y-5z =0 5x-y+42=0 (a) Find the angle between the two planes. (Round your answer to two decimal places. If the planes do not intersect, enter DNE) (b) Find parametric equations of their line of intersection. (Let z = t, then solve for x(t) and y(t) in terms of. If the planes do not intersect, enter DNE.) x(t), y(t), z(t) -( Need Help? LReadItJ111 Talk to a

Solution

Given

x + y – 5z = 0 =======> (1, 1, -5) = A

5x – y + 4z = 0 ========> (5, -1, 4) = B

A.B = 5 – 1 – 20 = -16

|A| = sqrt(27)

|B| = sqrt(42)

Then using cos = A.B/(|A|.|B|) = -16/(sqrt(27)*sqrt(42)) = -0.475

= arccos(-0.475) = 118.4 degree