Direction Cosines

Direction Cosines

If a vector $$\vec a$$ makes angles $$\alpha,\beta,\gamma$$ with the positive $$x,y,z$$ axes respectively, then:

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

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

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

Terminology

- $$\alpha,\beta,\gamma$$: Direction angles.

- $$a_x,a_y,a_z$$: Components of the vector.

Usage

- Used to determine the direction of a vector in three-dimensional space.