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NDA 2018 Maths · Mathematics · Vector Algebra · easy

If |vec a|=2 and |vec b|=3, then |vec a×vec b|^2+(vec a·vec b)^2 equals

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If ∣a⃗∣=2|\vec a|=2 and ∣b⃗∣=3|\vec b|=3, then ∣a⃗×b⃗∣2+(a⃗⋅b⃗)2|\vec a\times\vec b|^2+(\vec a\cdot\vec b)^2 equals
  1. A. 1313
  2. B. 66
  3. C. 3636
  4. D. 2525
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Answer: (C) 3636

By Lagrange's identity, ∣a⃗×b⃗∣2+(a⃗⋅b⃗)2=∣a⃗∣2∣b⃗∣2(sin⁡2θ+cos⁡2θ)=4×9=36|\vec a\times\vec b|^2+(\vec a\cdot\vec b)^2=|\vec a|^2|\vec b|^2\left(\sin^2\theta+\cos^2\theta\right)=4\times9=36. It does not depend on the angle, which is the point of the question.
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Original question written in the NDA 2018 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