The value of \(\lambda\), so that vectors \(2\hat{\imath}-\lambda\hat{\jmath}+4\hat{k}\), \(\hat{\imath}+\hat{\jmath}-\hat{k}\), and \(-2\hat{\imath}+3\hat{\jmath}+7\hat{k}\) are co-planar, is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → −8
Three vectors are coplanar when their scalar triple product is zero:
\( \displaystyle \begin{vmatrix}2 & -\lambda & 4\\ 1 & 1 & -1\\ -2 & 3 & 7\end{vmatrix} = 0 \)
Expanding along the first row:
\(2(7+3)+\lambda(7-2)+4(3+2) = 0\)
\(20+5\lambda+20 = 0\)
\(5\lambda = -40\)
\(\lambda = -8\)
Note: This topic was not in the CUET 2026 syllabus.