Question

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