NDA 2021 Maths · Mathematics · Three Dimensional Geometry · medium

The cosine of the acute angle between the planes x+y+z=1 and x-y+z=3 is

Single correct option

The cosine of the acute angle between the planes

x+y+z=1

and

x-y+z=3

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Answer: (A) $\dfrac13$

The angle between planes is the angle between their normals

(1,1,1)

and

(1,-1,1)

\cos\theta=\dfrac{1-1+1}{\sqrt3\sqrt3}=\dfrac13

. The right-hand sides

1

and

3

play no part.

Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake