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NDA 2021 Maths · Mathematics · Vector Algebra · medium

If vec a·vec b=|vec a×vec b| for two non-zero vectors, the angle between them is

Single correct option

If a⃗⋅b⃗=∣a⃗×b⃗∣\vec a\cdot\vec b=|\vec a\times\vec b| for two non-zero vectors, the angle between them is
  1. A. 30∘30^\circ
  2. B. 60∘60^\circ
  3. C. 90∘90^\circ
  4. D. 45∘45^\circ
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Answer: (D) 45∘45^\circ

With θ\theta the angle, ∣a⃗∣∣b⃗∣cos⁡θ=∣a⃗∣∣b⃗∣sin⁡θ|\vec a||\vec b|\cos\theta=|\vec a||\vec b|\sin\theta, so tan⁡θ=1\tan\theta=1 and θ=45∘\theta=45^\circ. At 90∘90^\circ the dot product would be zero while the cross product is not.
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Original question written in the NDA 2021 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