PrepRung
Sign inSign up free

NDA 2025 Maths · Mathematics · Vector Algebra · medium

If vec a·vec b=0 and vec a×vec b=vec 0, then

Single correct option

If a⃗⋅b⃗=0\vec a\cdot\vec b=0 and a⃗×b⃗=0⃗\vec a\times\vec b=\vec 0, then
  1. A. a⃗⊥b⃗\vec a\perp\vec b only
  2. B. a⃗∥b⃗\vec a\parallel\vec b only
  3. C. a⃗=0⃗\vec a=\vec0 or b⃗=0⃗\vec b=\vec0
  4. D. a⃗=b⃗\vec a=\vec b
Show answer and solution

Answer: (C) a⃗=0⃗\vec a=\vec0 or b⃗=0⃗\vec b=\vec0

a⃗⋅b⃗=0\vec a\cdot\vec b=0 means cos⁡θ=0\cos\theta=0 or one vector is zero, and a⃗×b⃗=0⃗\vec a\times\vec b=\vec0 means sin⁡θ=0\sin\theta=0 or one vector is zero. Both cannot hold for non-zero vectors because sin⁡θ\sin\theta and cos⁡θ\cos\theta are never zero together. So at least one vector is the zero vector.
Report a mistake

Original question written in the NDA 2025 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