Question

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

• A. 425
• B. 375
• C. 325
• D. 300

Answer 1

The correct option is D 300

${\left\{\right(a+3b)\times (3a-b\left)\right\}}^2={\{3a\times a-a\times b+9b+a-3b\times b\}}^2$
$={\left\{10\right(b\times a\left)\right\}}^2={10}^2|b{|}^2|a{|}^{2}si{n}^2(a,b)=100\left(2{)}^2\right(1{)}^{2}si{n}^2\left({120}^{\circ }\right)=400{\left(\frac{\sqrt{3}}{2}\right)}^2=300$