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If the vectors $2 \mathbf{i}-\mathbf{j}+\mathbf{k}, \mathbf{i}+2 \mathbf{j}-3 \mathbf{k}$ and $3 \mathbf{i}+\lambda \mathbf{j}+5 \mathbf{k}$ be coplanar, then $\lambda=$
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Verified Answer
The correct answer is:
-4
If the given vectors are coplanar, then their scalar triple product is zero.
$\left|\begin{array}{ccc}
2 & -1 & 1 \\
1 & 2 & -3 \\
3 & \lambda & 5
\end{array}\right|=0 \Rightarrow \lambda=-4$
$\left|\begin{array}{ccc}
2 & -1 & 1 \\
1 & 2 & -3 \\
3 & \lambda & 5
\end{array}\right|=0 \Rightarrow \lambda=-4$
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