# Vectors

# Basic Concepts of Vectors

**Vectors**can be expressed in terms of their components. A two-dimensional vector, for example, can be expressed as (x, y), while a three-dimensional vector can be described as (x, y, z).**Magnitude**of a vector: The size or length of a vector is referred to as the magnitude, represented as |v|. It can be calculated using the Pythagorean theorem.

# Vector Operations

**Vector addition**: Vectors are added by adding corresponding components. If**a**= (x1, y1) and**b**= (x2, y2), then**a + b**= (x1 + x2, y1 + y2).**Scalar multiplication**: A vector can be multiplied by a scalar (a number). If**a**= (x, y) and k is a scalar, then k**a**= (kx, ky).

# Vector Applications

**Position vectors**: This identifies a point in space relative to an origin. If O is the origin and P is the point (x, y), the position vector OP = (x, y).**Displacement vectors**: This describes movement from one point in space to another.

# Properties of Vectors

- Vectors are
**equal**if they have the same magnitude and direction, regardless of their initial point. - The
**zero vector**, denoted by 0 or 0**, has a magnitude of zero and is undefined .

Remember, **vectors represent quantities with both magnitude and direction**. They are used to describe various mathematical and physical concepts, including force, velocity, and displacement.