Question

The vector is given by R=3i+4j-5k find the magnitude of the xy component and the angle between R and xy axis

Answer 1

The magnitude of the xy component is given by

$$R_{xy}=\sqrt{3^2+4^2}=5$$

The angle between R and xy axis

$$\theta=\cos^{-1}\frac{R_{xy}}{R}$$

$$\theta=\cos^{-1}\frac{5}{5\sqrt{2}}=45^\circ$$