Question

What is the plane equation involved in the formula sinθ=\(\frac {a1a+b1b+c1c}{\sqrt {a^2+b^2+c^2} \sqrt{a1^2+b1^2+c1^2 }}\)?

(a) a1x – b1y + c1z + d1 = 0

(b) a1x^2 + b1y^2 + c1z^2 + d1 = 0

(c) ax + by + cz+ d = 0

(d) a1x + b1y + c1z + d1 = 0 and ax + by + cz + d = 0

This question was addressed to me during an internship interview.

The query is from Three Dimensional Geometry in chapter Three Dimensional Geometry of Mathematics – Class 12

Answer 1

Correct choice is (c) ax + by + cz+ d = 0

Explanation: The angle between a line and a plane is the complement of the angle between the line L and a normal line to the plane π. If θ is the angle between line whose ratios are a1, b1, c1 and the plane ax + by + cz + d = 0 then sin θ=\(\frac {a1a+b1b+c1c}{\sqrt {a^2+b^2+c^2} \sqrt{a1^2+b1^2+c1^2 }}\).