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What is a Vector?

In these lessons, we will learn what are vectors and how they can be expressed.

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More Lessons on Vectors

Scalar quantities are quantities that have only magnitudes such as time, area and distance.

Vector quantities are quantities that have both magnitudes and directions such velocity (speed and direction), force and acceleration.

A vector can be represented by a directed line segment, whose direction is given by the arrow and the length shows the magnitude of the vector.

The vectors can be denoted by or AB or or or a.

A is called the initial point and B is called the terminal point of .

The magnitude of a vector is the length of the corresponding segment. The magnitude of is denoted by .

A vector can be written as an ordered pair called a column vector

Consider the line PQ in the diagram. The line represents the translation of P to Q, which is 2 right and 3 up.

This can be written as the ordered pair


Express as a column vector.


The translation of C to D is 4 right and 3 down.


An introduction to vectors
This video introduces vectors - what they are and how they are expressed.
Magnitude, direction, graphing/mapping, Unit Vectors.

A video revising vectors at higher GCSE Maths level
Vectors with numbers
Magnitude of a Vector
Algebraic Vectors
Parallel Vectors

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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