NDA 2026 · PYQ · Vector Algebra · medium
What is the value of r²?
- A.4
- B.2
- C.1
- D.1/2✓ Correct
Since c is a unit vector: |c|² = 1 = p² + q² + r²|a × b|² + cross terms. Since a ⊥ b, |a × b| = |a||b|sin(π/2) = 1. Cross terms involve a·b = 0, a·(a×b) = 0, b·(a×b) = 0. So 1 = p² + q² + r² = 1/4 + 1/4 + r². Thus r² = 1 − 1/2 = 1/2.
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