A) \[\frac{\sqrt{3}}{2}\]
B) \[\sqrt{\frac{3}{2}}\]
C) \[\sqrt{6}\]
D) \[3\sqrt{6}\]
Correct Answer: B
Solution :
Vector perpendicular to plane containing the vectors \[\hat{i}+\hat{j}+\hat{k}\And \hat{i}+2\hat{j}+3\hat{k}\] is parallel to vector\[=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & 1 & 1 \\ 1 & 2 & 3 \\ \end{matrix} \right|=\hat{i}-2\hat{j}+\hat{k}\] \[\therefore \] Required magnitude of projection \[=\frac{\left| (2\hat{i}+3\hat{j}+\hat{k}).(\hat{i}-2\hat{j}+\hat{k}) \right|}{\left| \hat{i}-2\hat{j}+\hat{k} \right|}\] \[=\frac{\left| 2-6+1 \right|}{\left| \sqrt{6} \right|}=\frac{3}{\sqrt{6}}=\sqrt{\frac{3}{2}}\]
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