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NDA 2019 Maths · Mathematics · Vector Algebra · medium

If |vec a×vec b|=12 and vec a·vec b=5, then |vec a| |vec b| is equal to

Single correct option

If ∣a⃗×b⃗∣=12|\vec a\times\vec b|=12 and a⃗⋅b⃗=5\vec a\cdot\vec b=5, then ∣a⃗∣ ∣b⃗∣|\vec a|\,|\vec b| is equal to
  1. A. 1717
  2. B. 77
  3. C. 1313
  4. D. 119\sqrt{119}
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Answer: (C) 1313

Since ∣a⃗×b⃗∣=∣a⃗∣∣b⃗∣sin⁡θ|\vec a\times\vec b|=|\vec a||\vec b|\sin\theta and a⃗⋅b⃗=∣a⃗∣∣b⃗∣cos⁡θ\vec a\cdot\vec b=|\vec a||\vec b|\cos\theta, squaring and adding gives (∣a⃗∣∣b⃗∣)2=122+52=169(|\vec a||\vec b|)^2=12^2+5^2=169. So ∣a⃗∣∣b⃗∣=13|\vec a||\vec b|=13. Adding 12+5=1712+5=17 ignores the squares.
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Original question written in the NDA 2019 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