Question

Two forces $\overrightarrow{F_1}=(2\hat{i}+2\hat{j})N$ and $\overrightarrow{F_2}=(3\hat{j}+4\hat{k})N$ are acting on a particle. The angle between $\overrightarrow{F_1}\text{and}\overrightarrow{F_2}$ is

• A. $\theta =co{s}^{-1}\left(\frac{3}{2\sqrt{5}}\right)$
• B. $\theta =co{s}^{-1}\left(\frac{3}{5\sqrt{2}}\right)$
• C. $\theta =co{s}^{-1}\left(\frac{2}{3\sqrt{5}}\right)$
• D. $\theta =co{s}^{-1}\left(\frac{\sqrt{3}}{5}\right)$

Answer 1

The correct option is B $\theta =co{s}^{-1}\left(\frac{3}{5\sqrt{2}}\right)$

$\cos \theta =\frac{\overrightarrow{F_1}.\overrightarrow{F_2}}{|\overrightarrow{F_1}||\overrightarrow{F_2}|}=\frac{(2\hat{i}+2\hat{j}).(3\hat{j}+4\hat{k})}{\sqrt{2^2+2^2}\sqrt{3^2+4^2}}=\frac{6}{5\sqrt{8}}$
$\Rightarrow \theta ={\cos }^{-1}\left(\frac{3}{5\sqrt{2}}\right)$