Question

If $|a|=3,|b|=4$ and the angle between $a$ and b is $120^{\circ }$, then $|4a+3b|$ is equal to

• A. 25
• B. 7
• C. 13
• D. 12

Answer 1

Answer: (D)

Given, $|a|=3,|b|=4$ and
angle between $a$ and $b=120^{\circ }$.
$\therefore |4a+3b{|}^2=(4a+3b)\cdot (4a+3b)$
$\Rightarrow =16|a{|}^2+9|b{|}^2+24a\cdot b$
$=16|a{|}^2+9|b{|}^2+24|a||b|\cos \theta$
$=16(3{)}^2+9(4{)}^2+24\times 3\times 4\times \cos 120^{\circ }$
$=16\times 9+9\times 16+24\times 12\times \left(\frac{-1}{2}\right)$
$=144+144-144=144$
So, $|4a+3b|=\sqrt{144}=12$