Vector Components from Direction Cosines

Vector Components from Direction Cosines

If $$|\vec a|=a$$, then:

$$a_x=a\cos\alpha$$

$$a_y=a\cos\beta$$

$$a_z=a\cos\gamma$$

Therefore:

$$\vec a=a(\cos\alpha\hat i+\cos\beta\hat j+\cos\gamma\hat k)$$

Usage

- Used to construct a vector when its magnitude and direction angles are known.