A vector is a mathematical object that has both magnitude (length or size) and direction. It is often represented graphically as an arrow in a coordinate system, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction. Number of elements of a vector is called dimensionality. Key characteristics:

• Magnitude (or length): The size or amount of the vector, often denoted by the symbol ||v|| or |v|.
• Direction: The orientation of the vector in space, often represented by the unit vector (a vector with a magnitude of 1) in the same direction.
• Components: The vector can be broken down into its component parts, often represented as (x, y) in 2-dimensional space or (x, y, z) in 3-dimensional space. Notation:
• Vectors are often denoted by boldface letters, such as v or a.
• The magnitude of a vector v is denoted by ||v|| or |v|.
• The unit vector in the same direction as v is denoted by v/||v|| or û. Examples:
• A displacement vector: an object moves from point A to point B, the vector represents the direction and distance of the movement.
• A force vector: a force applied to an object, the vector represents the direction and magnitude of the force.

#Vector Operations

#Vector Addition

#Scalar Multiplication

#Vector Subtraction

#Vector Linear Combination