Question:
If the vectors \(2\hat{i}+3\hat{j}+\hat{k}\) and \(4\hat{i}-\hat{j}+2\hat{k}\) are perpendicular, the value of \(\lambda\) in \(\lambda\hat{i}+2\hat{j}+3\hat{k}\) is:
If the vectors \(2\hat{i}+3\hat{j}+\hat{k}\) and \(4\hat{i}-\hat{j}+2\hat{k}\) are perpendicular, the value of \(\lambda\) in \(\lambda\hat{i}+2\hat{j}+3\hat{k}\) is:
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Perpendicular vectors have zero dot product.
Updated On: Jan 5, 2026
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The Correct Option is A
Solution and Explanation
For perpendicular vectors,
\[
(\lambda,2,3)\cdot(4,-1,2)=0
\Rightarrow 4\lambda-2+6=0
\Rightarrow \lambda=-1
\]
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