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NDA 2017 Maths · Mathematics · Vector Algebra · medium

The vectors phat i+hat j+hat k and hat i+phat j+hat k make an angle of 60^° with each other. The non-zero value of p is

Single correct option

The vectors pi^+j^+k^p\hat i+\hat j+\hat k and i^+pj^+k^\hat i+p\hat j+\hat k make an angle of 60∘60^\circ with each other. The non-zero value of pp is
  1. A. 22
  2. B. 11
  3. C. 44
  4. D. −2-2
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Answer: (C) 44

cos⁡60∘=2p+1p2+2=12\cos60^\circ=\frac{2p+1}{p^2+2}=\frac12 gives p2+2=4p+2p^2+2=4p+2, so p(p−4)=0p(p-4)=0. The non-zero root is p=4p=4. The root p=0p=0 is excluded by the question, and p=2p=2 gives cos⁡θ=56\cos\theta=\frac56.
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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