The magnitude of the projection of the vector $2 \hat{i}+3 \hat{j}+\hat{k}$ on the vector perpendicular to the plane containing the vectors $\hat{i}+\hat{j}+\hat{k}$ and $\hat{i}+2 \hat{j}+3 \hat{k}$ is

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Aicharya · Accepted Answer

$\begin{aligned} & \frac{|(2 \hat{i}+3 \hat{j}+\hat{k}) \cdot\{(\hat{i}+\hat{j}+\hat{k}) 	imes(\hat{i}+2 \hat{j}+3 \hat{k})\}|}{|(\hat{i}+\hat{j}+\hat{k}) 	imes(\hat{i}+2 \hat{j}+3 \hat{k})|} \ & =\frac{|(2 \hat{i}+3 \hat{j}+\hat{k}) \cdot(\hat{i}-2 \hat{j}+\hat{k})|}{|\hat{i}+\hat{j}+\hat{k}|} \ & =\frac{|2-6+1|}{\sqrt{1^2+(-2)^2+1^2}}=\frac{3}{\sqrt{6}}=\sqrt{\frac{3}{2}}\end{aligned}$

The magnitude of the projection of the vector $2 \hat{i}+3 \hat{j}+\hat{k}$ on the vector perpendicular to…

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