If three vectors 2î - ĵ + k̂, î + 2ĵ - 3k̂ and 3î + λĵ + 5k̂ are co-planar, then λ is:
The vectors are coplanar when their scalar triple product is 0:
\(\begin{vmatrix} 2 & -1 & 1 \\ 1 & 2 & -3 \\ 3 & \lambda & 5 \end{vmatrix} = 2(10 + 3\lambda) + 1(5 + 9) + 1(\lambda - 6) = 28 + 7\lambda = 0\)
\(\lambda = -4\)
Answer: (D) −4
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