Question

If $13\overline{a}=3\overline{i}+4\overline{j}+12\overline{k},13\overline{b}=4\overline{i}-12\overline{j}+3\overline{k},13\overline{c}=12\overline{i}+3\overline{j}-4\overline{k}$, then the value of $\overline{a}\times \overline{b}$ in terms of $\overrightarrow{c}$ is

• A. $\overline{c}$
• B. $5\overline{c}$
• C. $13\overline{c}$
• D. $15\overline{c}$

Answer 1

The correct option is A $\overline{c}$

$\overrightarrow{a}\times \overrightarrow{b}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 4& 12\\ 4& -12& 3\end{array}\right|=\frac{13\times 12\hat{i}+39\hat{j}-52\hat{k}}{169}$
$\overrightarrow{a}\times \overrightarrow{b}=\frac{12}{13}\hat{i}+\frac{3}{13}\hat{j}-\frac{4}{13}\hat{k}$
$=\overrightarrow{c}$