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NDA 2016 Maths · Mathematics · Vector Algebra · medium

If |vec a|=3, |vec b|=4 and |vec a+vec b|=5, then the angle between vec a and vec b is

Single correct option

If ∣a⃗∣=3|\vec a|=3, ∣b⃗∣=4|\vec b|=4 and ∣a⃗+b⃗∣=5|\vec a+\vec b|=5, then the angle between a⃗\vec a and b⃗\vec b is
  1. A. 0∘0^\circ
  2. B. 90∘90^\circ
  3. C. 60∘60^\circ
  4. D. 45∘45^\circ
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Answer: (B) 90∘90^\circ

∣a⃗+b⃗∣2=∣a⃗∣2+∣b⃗∣2+2a⃗⋅b⃗|\vec a+\vec b|^2=|\vec a|^2+|\vec b|^2+2\vec a\cdot\vec b gives 25=9+16+2a⃗⋅b⃗25=9+16+2\vec a\cdot\vec b, so a⃗⋅b⃗=0\vec a\cdot\vec b=0. This is the Pythagorean 3-4-5 case, so the vectors are perpendicular.
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Original question written in the NDA 2016 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