The equation of the plane bisecting the

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Three-dimensional Geometry

Question:

The equation of the plane bisecting the acute angle between the planes 2x – y + 2z + 3 = 0 and 3x – 2y + 6z + 8 = 0 is

Options:

23x – 13y + 32z + 45 = 0

5x – y – 4z = 3

5x – y – 4z + 45 = 0

23x – 13y + 32z + 3 = 0

Correct Answer:

23x – 13y + 32z + 45 = 0

Explanation:

a₁a₁ + b₁b₂ + c₁c₂ = 6 + 2 + 12 is positive

so that the acute angle bisector is $\frac{2x-y+2z+3}{3}=-\frac{3x-2y+6z+8}{7}$

⇒ 23x - 13y + 32z + 45 = 0.

Hence (A) is the correct answer.