જો \(\vec{P}=3 \tilde{i}+\sqrt{3} \hat{j}+2 \hat{k}\) અને \(\vec{Q}=4 \hat{i}+\sqrt{3} \hat{j}+2.5 \hat{k}\) હોય, તો \(\vec{P} \times \vec{Q}\) ની દિશામાં એકમ સદિશ \(\frac{1}{x}(\sqrt{3} i+\hat{j}-2 \sqrt{3} \hat{k})\) છે . \(x\) નું મૂલ્ય \(..........\) થશે.

If \(\overrightarrow{ P }=3 \hat{ i }+\sqrt{3} \hat{ j }+2 \hat{ k }\) and \(\overrightarrow{ Q }=4 \hat{ i }+\sqrt{3} \hat{ j }+2.5 \hat{ k }\) then, The unit vector in the direction of \(\overrightarrow{ P } \times \overrightarrow{ Q }\) is \(\frac{1}{x}(\sqrt{3} \hat{i}+\hat{j}-2 \sqrt{3} \hat{k})\). The value of \(x\) is
\(\begin{array}{l}\overrightarrow{ P } \times \overrightarrow{ Q }=\left|\begin{array}{ccc}\hat{ i } & \hat{ j } & \hat{ k } \\ 3 & \sqrt{3} & 2 \\ 4 & \sqrt{3} & 2.5\end{array}\right|=\sqrt{3} \frac{\hat{ i }}{2}+\frac{\hat{ j }}{2}-\sqrt{3} \hat{ k } \\ \Rightarrow \frac{\overrightarrow{ P } \times \overrightarrow{ Q }}{|\overrightarrow{ P } \times \overrightarrow{ Q }|}=\frac{1}{2}\left(\sqrt{3} \frac{\hat{ i }}{2}+\frac{\hat{ j }}{2}-\sqrt{3} \hat{ k }\right)\end{array}\)
\( =\frac{1}{4}(\sqrt{3} \hat{ i }+\hat{ j }-2 \sqrt{3} \hat{ k })\)
The unit vector in the direction of \(\overrightarrow{ P } \times \overrightarrow{ Q }\) is \(\frac{1}{x}(\sqrt{3} \hat{i}+\hat{j}-2 \sqrt{3} \hat{k})\)
hence \( x=4\)