Vectors

This lesson covers vectors as a data structure and mathematical concept, as specified in the OCR A-Level Computer Science (H446) specification, section 1.4. Vectors are used in graphics, physics simulations, machine learning, and many other areas of computing.

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What is a Vector?

A vector is a mathematical object that has both magnitude (size) and direction. In computing, vectors are represented as ordered lists of numbers.

Vectors vs Scalars

Concept	Description	Example
Scalar	A single number (magnitude only)	Temperature: 20, Speed: 5
Vector	An ordered list of numbers (magnitude and direction)	Position: (3, 4), Velocity: (2, -1, 5)

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Representing Vectors

Vectors can be represented as lists or arrays of numbers. A vector with n components is called an n-dimensional vector.

Examples

2D vector: v = (3, 4)        -- 2 components
3D vector: w = (1, -2, 5)    -- 3 components
4D vector: u = (1, 0, 3, 7)  -- 4 components

As a Dictionary/Function

A vector can also be thought of as a function that maps indices to values:

• v(0) = 3, v(1) = 4