If $|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=3,|\overline{\mathrm{c}}|=4$ and…
If $|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=3,|\overline{\mathrm{c}}|=4$ and $\overline{\mathrm{a}}$ is perpendicular to $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ such that angle between $\bar{b}$ and $\bar{c}$ is $\frac{5 \pi}{6}$, then $[\bar{a} \bar{b} \bar{c}]=$
25
10
30
20
Solution
$[\vec{a} \vec{b} \vec{c}]=|\vec{a}||\vec{b}||\vec{c}| \cdot(\cos$ of angle between $\vec{a}$ and $\vec{b} \times \vec{c})$.(sin of angle between $\vec{b}$ and $\vec{c}$ )
$\begin{aligned} & =5 \times 3 \times 4 \times \cos 0 \times \sin \left(\frac{5 \pi}{6}\right) \\ & =60 \times 1 \times \frac{1}{2}=30\end{aligned}$