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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2012 · Mathematics · Three Dimensional Geometry

What is the cosine of angle between the planes x+y+z+1=0 and 2 x-2...

What is the cosine of angle between the planes x+y+z+1=0x+y+z+1=0 and 2x−2y+2z+1=02 x-2 y+2 z+1=0 ?

Options

  1. A1/2
  2. B1/3
  3. C2/3
  4. DNone of the above

Correct answer

B. 1/3

Step-by-step solution

cos⁡θ=1(2)+1(−2)+1(2)12+12+12⋅22+(−2)2+22=2323=13\cos \theta=\frac{1(2)+1(-2)+1(2)}{\sqrt{1^2+1^2+1^2} \cdot \sqrt{2^2+(-2)^2+2^2}}=\frac{2}{\sqrt{3} 2 \sqrt{3}}=\frac{1}{3}.
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