- Home
- Standard 11
- Physics
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.
$3$
$2$
$1$
$4$
Solution
$\begin{array}{l}\overrightarrow{ P } \times \overrightarrow{ Q }=\left|\begin{array}{ccc}\hat{ i } & \hat{ j } & \hat{ k } \\ 3 & \sqrt{3} & 2 \\ 4 & \sqrt{3} & 2.5\end{array}\right|=\sqrt{3} \frac{\hat{ i }}{2}+\frac{\hat{ j }}{2}-\sqrt{3} \hat{ k } \\ \Rightarrow \frac{\overrightarrow{ P } \times \overrightarrow{ Q }}{|\overrightarrow{ P } \times \overrightarrow{ Q }|}=\frac{1}{2}\left(\sqrt{3} \frac{\hat{ i }}{2}+\frac{\hat{ j }}{2}-\sqrt{3} \hat{ k }\right) \\ =\frac{1}{4}(\sqrt{3} \hat{ i }+\hat{ j }-2 \sqrt{3} \hat{ k }) \quad x =4\end{array}$
