Angle Between a Vector and a Coordinate Axis

Angle Between a Vector and a Coordinate Axis

If:

$$\vec a=a_x\hat i+a_y\hat j+a_z\hat k$$

then the angle $$\alpha$$ with the x-axis satisfies:

$$\cos\alpha=\frac{a_x}{|\vec a|}$$

Similarly:

$$\cos\beta=\frac{a_y}{|\vec a|}$$

$$\cos\gamma=\frac{a_z}{|\vec a|}$$

Usage

- Used to determine direction angles from vector components.