Question

Find the angle between 2x + 3y – 2z + 4 = 0 and (2, 1, 1).

(a) 38.2

(b) 19.64

(c) 89.21

(d) 29.34

The question was asked in examination.

The origin of the question is Three Dimensional Geometry in chapter Three Dimensional Geometry of Mathematics – Class 12

Answer 1

Right choice is (d) 29.34

Easy explanation: Angle between a plane and a line sin θ=\(\frac {a1a+b1b+c1c}{\sqrt {a^2+b^2+c^2} \sqrt{a1^2+b1^2+c1^2 }}\)

sinθ = 0.49

θ = sin^-1(0.49)

θ = 29.34