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NDA 2017 Maths · Mathematics · Vector Algebra · medium

If |vec a|=1, |vec b|=2 and the angle between them is 120^°, then |2vec a+vec b| equals

Single correct option

If ∣a⃗∣=1, ∣b⃗∣=2|\vec a|=1,\ |\vec b|=2 and the angle between them is 120∘120^\circ, then ∣2a⃗+b⃗∣|2\vec a+\vec b| equals
  1. A. 44
  2. B. 232\sqrt3
  3. C. 22
  4. D. 66
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Answer: (C) 22

a⃗⋅b⃗=1⋅2cos⁡120∘=−1\vec a\cdot\vec b=1\cdot2\cos120^\circ=-1. Then ∣2a⃗+b⃗∣2=4∣a⃗∣2+∣b⃗∣2+4a⃗⋅b⃗=4+4−4=4|2\vec a+\vec b|^2=4|\vec a|^2+|\vec b|^2+4\vec a\cdot\vec b=4+4-4=4, so the length is 22. Ignoring the negative dot product gives 12=23\sqrt{12}=2\sqrt3, and adding magnitudes gives 44.
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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