Three Dimensional Geometry · Class 12 · CBSE · Science Mathematics

The acute angle between the planes 2x - y + 2z = 5 and x + 2y + 2z = 7 has cosine equal to:

Practice question from Three Dimensional Geometry (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-BF04BB

The acute angle between the planes 2x - y + 2z = 5 and x + 2y + 2z = 7 has cosine equal to:

  1. A.1/9
  2. B.2/9
  3. C.4/9Correct answer
  4. D.8/9

Solution

The normal vectors are (2,−1,2)(2,-1,2) and (1,2,2)(1,2,2). Therefore, cos⁡θ=∣2(1)+(−1)(2)+2(2)∣99=49\cos\theta=\frac{|2(1)+(-1)(2)+2(2)|}{\sqrt{9}\sqrt{9}}=\frac{4}{9}.

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