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NDA 2017 Maths · Mathematics · Vector Algebra · medium

Examine the following assertions about non-zero vectors vec p,vec q,vec r: 1. vec p·vec q=0 for every pair of mutually perpendicular vectors. 2. If…

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Examine the following assertions about non-zero vectors p⃗,q⃗,r⃗\vec p,\vec q,\vec r:
1. p⃗⋅q⃗=0\vec p\cdot\vec q=0 for every pair of mutually perpendicular vectors.
2. If p⃗×q⃗=p⃗×r⃗\vec p\times\vec q=\vec p\times\vec r, then q⃗=r⃗\vec q=\vec r.
Which of the statements given above is/are correct?
  1. A. 11 only
  2. B. 22 only
  3. C. Both 11 and 22
  4. D. Neither 11 nor 22
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Answer: (A) 11 only

1 is true: perpendicular non-zero vectors have cos⁡90∘=0\cos90^\circ=0, so the dot product is zero. 2 is false: p⃗×(q⃗−r⃗)=0⃗\vec p\times(\vec q-\vec r)=\vec0 only shows that q⃗−r⃗\vec q-\vec r is parallel to p⃗\vec p (for example r⃗=q⃗+p⃗\vec r=\vec q+\vec p). Only assertion 1 is correct; vector products cannot be cancelled.
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Original question written in the NDA 2017 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