Vectors

A vector represents a quantity with both magnitude and direction.

Example

A two-dimensional vector can be written as:

$$\mathbf{v} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}$$

Magnitude

The magnitude of this vector is:

$$|\mathbf{v}| = \sqrt{3^2 + 4^2} = 5$$

Important Operations

• Vector addition
• Scalar multiplication
• Dot product
• Cross product