Question

If $a=3i+3j+4k,b=i+j+k$ and $c=4i+2j+3k$ then $\frac{1}{5\sqrt{2}}\left|a\times \left(b\times c\right)\right|$ is equal to

• A. $8\sqrt{2}$
• B. $9\sqrt{2}$
• C. $10\sqrt{2}$
• D. 2

Answer 1

Answer: (D)

2

We have,

$\begin{array}{c}\left|\overline{a}\left(\overline{b}\times \overline{c}\right)\right|=\left|\left(\overline{a}.\overline{c}\right)\overline{b}-\left(\overline{a}.\overline{b}\right)\overline{c}\right|\\ =\left|30\overline{b}-10\overline{c}\right|\\ =\left|-10\hat{i}+10\hat{j}\right|\\ =\sqrt{200}\\ =10\sqrt{2}\\ \frac{1}{5\sqrt{2}}\left|\overline{a}\left(\overline{b}\times \overline{c}\right)\right|=\frac{10\sqrt{2}}{5\sqrt{2}}=2\end{array}$

Then,

Option $D$ is correct answer.