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NDA 2017 Maths · Mathematics · Vector Algebra · medium

The vectors hat i+2hat j+3hat k and 2hat i+4hat j+6hat k are collinear. 2. The vectors hat i+hat j, hat j+hat k and hat k+hat i are coplanar.

Single correct option

Consider the following statements:
1. The vectors i^+2j^+3k^\hat i+2\hat j+3\hat k and 2i^+4j^+6k^2\hat i+4\hat j+6\hat k are collinear.
2. The vectors i^+j^, j^+k^\hat i+\hat j,\ \hat j+\hat k and k^+i^\hat k+\hat i are coplanar.
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
Show answer and solution

Answer: (A) 11 only

1: the second vector is twice the first, so they are collinear. 2: the scalar triple product is ∣110011101∣=1(1)−1(0−1)+0=2≠0\begin{vmatrix}1&1&0\\0&1&1\\1&0&1\end{vmatrix}=1(1)-1(0-1)+0=2\ne0, so the three vectors are not coplanar. Only statement 1 is correct; coplanarity needs a zero determinant.
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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