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NDA 2018 Maths · Mathematics · Vector Algebra · medium

If vec a×vec b=vec 0, then either vec a=vec 0 or vec b=vec 0. 2. If vec a·vec b=0, then vec a and vec b are perpendicular or at least one of them is…

Single correct option

Consider the following statements:
1. If a⃗×b⃗=0⃗\vec a\times\vec b=\vec 0, then either a⃗=0⃗\vec a=\vec 0 or b⃗=0⃗\vec b=\vec 0.
2. If a⃗⋅b⃗=0\vec a\cdot\vec b=0, then a⃗\vec a and b⃗\vec b are perpendicular or at least one of them is the zero vector.
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (B) 2 only

Statement 1 is false: parallel non-zero vectors (for example i^\hat i and 2i^2\hat i) also have zero cross product. Statement 2 is true, since a⃗⋅b⃗=∣a⃗∣∣b⃗∣cos⁡θ=0\vec a\cdot\vec b=|\vec a||\vec b|\cos\theta=0 means a magnitude is zero or θ=90∘\theta=90^\circ. Hence 2 only.
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Original question written in the NDA 2018 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