Question

If $\overline{c}$ is perpendicular to $\overline{a}$ and $\overline{b}$ , $\left|\overline{a}\right|=3,\left|\overline{b}\right|=4,\left|\overline{c}\right|=5$ and the angle between $\overline{a}$ and $\overline{b}$ is $\frac{\pi }{6}$ then $\left[\overline{a}\overline{b}\overline{c}\right]=$

• A. $30\sqrt{3}$
• B. $30$
• C. $15$
• D. $15\sqrt{3}$

Answer 1

Answer: (B)

$30$

We have,

$\begin{array}{c}\left[\overline{a}\overline{b}\overline{c}\right]=\overline{c}\times \left(\overline{a}\times \overline{b}\right)\\ =\overline{c}\times \left(\overline{a}\times \overline{b}\right)\cos 0^0\\ =5\times 3\times 4\times \sin \frac{\pi }{6}\end{array}$

$=5\times 3\times 4\times \frac{1}{2}$

$=30$

Then,

Option $B$ is correct answer.