Question

Find the angle between 2x + 3y – 2z + 4 = 0 and 4x + 3y + 2z + 2 = 0.

(a) 38.2

(b) 19.64

(c) 89.21

(d) 54.54

I had been asked this question in final exam.

My query is from Three Dimensional Geometry in division Three Dimensional Geometry of Mathematics – Class 12

Answer 1

Correct choice is (d) 54.54

Explanation: Angle between two planes cos cos θ=\(\frac {a1a2+b1b2+c1c2}{\sqrt {a1^2+b1^2+c1^2} \sqrt {a2^2+b2^2+c2^2 }}\)

cos θ = 0.58

θ = cos^-1(0.58)

θ = 54.54