Vectors

Vectors

Any physical quantity that has both, magnitude and direction

Orthogonal vectors

Vectors that are perpendicular to each other. I.e. 90° b/w them.

Resultant of two Vectors

$$R=\sqrt{A^2+B^2+2AB\cos\theta}$$

Resultant when $\left\vert\overrightarrow{A}\right\vert=\left\vert\overrightarrow{B}\right\vert$

$$R=2A\cos\left(\frac{\theta}{2}\right)$$

Resultant when $\left\vert\overrightarrow{A}\right\vert-\left\vert\overrightarrow{B}\right\vert$

$$R=2A\sin\left(\frac{\theta}{2}\right)$$

Scalar Product

$$\overrightarrow{A}\cdot\overrightarrow{B}=AB\cos\theta$$

Vector Product

$$\overrightarrow{A}×\overrightarrow{B}=AB\sin\theta$$