NDA 2026 · PYQ · Vector Algebra · medium
Let a, b, c, a+b, b+c, a+b+c be unit vectors. What is the angle between a and b?
Answer
The correct answer is D: 2π/3. Since |a| = |b| = |a+b| = 1, we have |a+b|² = |a|² + |b|² + 2a·b = 1 + 1 + 2cos θ = 1. So 2cos θ = −1, giving cos θ = −1/2, hence θ = 2π/3.
- A.π/6
- B.π/4
- C.π/2
- D.2π/3✓ Correct
Since |a| = |b| = |a+b| = 1, we have |a+b|² = |a|² + |b|² + 2a·b = 1 + 1 + 2cos θ = 1. So 2cos θ = −1, giving cos θ = −1/2, hence θ = 2π/3.
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