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NDA 2025 Maths · Mathematics · Vector Algebra · medium

For two non-zero vectors, the dot product equals the magnitude of the cross product. The angle between the vectors is then

Single correct option

For two non-zero vectors, the dot product equals the magnitude of the cross product. The angle between the vectors is then
  1. A. 45∘45^\circ
  2. B. 30∘30^\circ
  3. C. 60∘60^\circ
  4. D. 90∘90^\circ
Show answer and solution

Answer: (A) 45∘45^\circ

∣a⃗∣∣b⃗∣cos⁡θ=∣a⃗∣∣b⃗∣sin⁡θ|\vec a||\vec b|\cos\theta=|\vec a||\vec b|\sin\theta gives tan⁡θ=1\tan\theta=1, so θ=45∘\theta=45^\circ. At 60∘60^\circ the cosine is half the sine times 3\sqrt3, and at 90∘90^\circ the dot product is zero while the cross product is largest. Equal cosine and sine occur only at 45∘45^\circ in the first quadrant.
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Original question written in the NDA 2025 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