If the vectors 3 i+ j+k and 2 i-j+8 k are perpendicular, then is … - Vidyadip

Question

If the vectors $3 \hat{i}+\lambda \hat{j}+\hat{k}$ and $2 \hat{i}-\hat{j}+8 \hat{k}$ are perpendicular, then $\lambda$ is equal to

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Answer

$(d) 14$
Explanation: given vectors $3 \hat{i}+\lambda \hat{j}+\hat{k}$ and $2 \hat{i}-\hat{j}+8 \hat{k}$ are perpendicular to each other
$ \Longrightarrow(3 \hat{i}+\lambda \hat{j}+\hat{k}) \cdot(2 \hat{i}-\hat{j}+8 \hat{k})=0$
$\Longrightarrow 6-\lambda+8=0 \Longrightarrow \lambda=14$

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