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NDA 2018 Maths · Mathematics · Vector Algebra · medium

The vectors hat i+2hat j-hat k, 2hat i+hat j+λhat k and hat i-hat j+2hat k are coplanar if λ equals

Single correct option

The vectors i^+2j^−k^\hat i+2\hat j-\hat k, 2i^+j^+λk^2\hat i+\hat j+\lambda\hat k and i^−j^+2k^\hat i-\hat j+2\hat k are coplanar if λ\lambda equals
  1. A. −1-1
  2. B. 00
  3. C. 22
  4. D. 11
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Answer: (D) 11

Coplanarity means the scalar triple product is zero: ∣12−121λ1−12∣=1(2+λ)−2(4−λ)−1(−2−1)=3λ−3\begin{vmatrix}1&2&-1\\2&1&\lambda\\1&-1&2\end{vmatrix}=1(2+\lambda)-2(4-\lambda)-1(-2-1)=3\lambda-3. Setting it to 0 gives λ=1\lambda=1. Sign errors in the middle cofactor give the other values.
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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