Question

If $|\overline{a}|=1,|\overline{b}|=2$ and the angle between $\overline{a}$ and $\overline{b}$ is ${120}^o$, then $\left\{\right(\overline{a}+3\overline{b})\times (3\overline{a}-\overline{b}){\}}^2=$

• A. 425
• B. 375
• C. 325
• D. 300

Answer 1

The correct option is D 300

$\left\{\right(\overline{a}+3\overline{b})\times (3\overline{a}-\overline{b}){\}}^2$

$=\{3\overline{a}\times \overline{a}-\overline{a}\times \overline{b}+9\overline{b}\times \overline{a}-3\overline{b}\times \overline{b}{\}}^2$

$=\left\{10\right(\overline{b}\times \overline{a}){\}}^2$

$=100|\overline{b}{|}^2|\overline{a}{|}^2{\sin }^2{120}^o$

$=100\times 1\times 4\times \frac{3}{4}$

$=300$