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NDA 2019 Maths · Mathematics · Vector Algebra · medium

The unit vectors vec a and vec b satisfy |vec a+vec b|=1. The angle between vec a and vec b is

Single correct option

The unit vectors a⃗\vec a and b⃗\vec b satisfy ∣a⃗+b⃗∣=1|\vec a+\vec b|=1. The angle between a⃗\vec a and b⃗\vec b is
  1. A. 60∘60^\circ
  2. B. 90∘90^\circ
  3. C. 120∘120^\circ
  4. D. 150∘150^\circ
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Answer: (C) 120∘120^\circ

∣a⃗+b⃗∣2=1+1+2cos⁡θ=1|\vec a+\vec b|^2=1+1+2\cos\theta=1, so cos⁡θ=−12\cos\theta=-\frac12 and θ=120∘\theta=120^\circ. The value 60∘60^\circ is the angle for which ∣a⃗−b⃗∣=1|\vec a-\vec b|=1 (equilateral triangle); the sign of the dot-product term decides between the two.
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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