Question

If a body placed at the origin is acted upon by a force $\overrightarrow{F}=(\hat{i}+\hat{j}+\sqrt{2}\hat{k})$, then which of the following statements are correct

• A. Magnitude of $\overrightarrow{F}$ is $(2+\sqrt{2})$
• B. Magnitude of $\overrightarrow{F}$ is $\left(2\sqrt{2}\right)$
• C. $\overrightarrow{F}$ makes an angle of ${45}^{\circ }$ with the z-axis.
• D. $\overrightarrow{F}$ makes an angle of ${30}^{\circ }$ with the z-axis.

Answer 1

Answer: (C)

$\overrightarrow{F}$ makes an angle of ${45}^{\circ }$ with the z-axis.

Magnitude $=F=\sqrt{1^2+1^2+{\left(\sqrt{2}\right)}^2}=2$
Angle with z-axis $={\cos }^{-1}\frac{F_z}{F}={\cos }^{-1}\frac{\sqrt{2}}{2}={45}^o$