# 2-D Vectors

## Key Questions

• A quantity possessing both magnitude and direction, represented by an arrow the direction of which indicates the direction of the quantity and the length of which is proportional to the magnitude.

• Resultant of vectors can be found using the law of cosines.

If A and B are two vectors with an angle between them equal to $\theta$ ($\theta < \pi$), their resultant R is given by,

$R = {\left[{A}^{2} + {B}^{2} + 2 A B C o s \theta\right]}^{\frac{1}{2}}$, this gives the magnitude of R.

If the vector R makes an angle $\alpha$ with vector A, then

$\alpha = \arctan \left[\frac{B C o s \theta}{A + B S \in \theta}\right]$