Vectors – GCSE Mathematics (Higher) OCR Revision

Understanding Vectors

A vector is a quantity that has both magnitude (size) and direction.
Vectors are usually represented by arrowed lines, where the length of the line indicates the magnitude and the arrow points in the direction of the vector.
Vectors can be added and subtracted according to the rules of vector addition and subtraction.
In Mathematics, vectors often carry letters, such as a or b, to distinguish them.

Each vector is usually represented by a letter written in bold or preceded by a small arrow when handwritten.
When represented numerically, vectors are put in column form, such as (8) for a one-dimensional vector, or (2 3) for a two-dimensional vector representing 2 in the x direction and 3 in the y direction.
The starting point of a vector is known as the tail and the endpoint is called the head.

Vectors can be added together to create a resultant vector. When adding vectors diagrammatically, place the tail of the second vector at the head of the first vector. The line drawn from the tail of the first vector to the head of the second vector is the resultant vector.
Subtraction of vectors is the same as adding a negative vector. Essentially, subtracting a vector is the same as adding its opposite.
Vectors can also be scaled, meaning multiplied by a scalar (a regular number). This changes the magnitude of the vector, but not the direction.
Multiplying a vector by a scalar is done by multiplying the magnitude of the vector by the scalar. For example, if vector a represents (2 3), then 2a would result in (4 6).

Vectors play a crucial role in fields such as physics, engineering, and computer graphics where both direction and magnitude are important.
They are useful for solving a number of real-world problems including velocity, force, and displacement issues.

As always, the best way to grasp the concept of vectors is to consistently work through problems and exercises. This helps understanding of how to apply vectors in various contexts.
It’s important to remember the distinction between vectors and scalars, and to remember to account for both magnitude and direction when dealing with vectors.