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NDA 2017 Maths · Mathematics · Three Dimensional Geometry · easy

The acute angle between the planes x+y=3 and y+z=5 is

Single correct option

The acute angle between the planes x+y=3x+y=3 and y+z=5y+z=5 is
  1. A. 30∘30^\circ
  2. B. 45∘45^\circ
  3. C. 60∘60^\circ
  4. D. 90∘90^\circ
Show answer and solution

Answer: (C) 60∘60^\circ

The normals are (1,1,0)(1,1,0) and (0,1,1)(0,1,1), so cos⁡θ=0+1+02⋅2=12\cos\theta=\frac{0+1+0}{\sqrt2\cdot\sqrt2}=\frac12 and θ=60∘\theta=60^\circ. The value 45∘45^\circ results from forgetting to divide by both magnitudes, while 90∘90^\circ would need a zero dot product.
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Original question written in the NDA 2017 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