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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2013 · Mathematics · Three Dimensional Geometry

What is the angle between the planes 2 x-y-2 z+1=0 and 3 x-4 y+5...

What is the angle between the planes 2x−y−2z+1=02 x-y-2 z+1=0 and 3x−4y+5z−3=03 x-4 y+5 z-3=0 ?

Options

  1. Aπ6\frac{\pi}{6}
  2. Bπ4\frac{\pi}{4}
  3. Cπ3\frac{\pi}{3}
  4. Dπ2\frac{\pi}{2}

Correct answer

D. π2\frac{\pi}{2}

Step-by-step solution

cos⁡θ=2(3)+(−1)(−4)+5(−2)22+12+2232+42+52=0θ=π2\begin{aligned} \cos \theta & =\frac{2(3)+(-1)(-4)+5(-2)}{\sqrt{2^2+1^2+2^2} \sqrt{3^2+4^2+5^2}}=0 \\ \theta & =\frac{\pi}{2}\end{aligned}
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