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What is a Vector?

The only difference between a vector and an ordinary scalar number like 6.2 or -12, is that unlike an ordinary number, a vector is not restricted to being a point along the length of a number line. That is to say, a vector is not restricted to existing in a single dimension.

So, while an ordinary number - a scalar, can tell you how far away the Moon is from your house right now; a vector can tell you its exact, three dimensional coordinates.

Vectors are basically scalars extended into three dimensions. While a scalar is a single coordinate on a number line, a vector is simply a set of coordinates, representing multiple dimensions.

So, while the scalar 6.2 represents a point 6.2 units right of the origin, a two dimensional vector written as (24, -5) might represent a point 24 units right of the origin and 5 units below the origin. Or, a four dimensional vector written as (4, 5, 1, 10) might represent a point, or in this case an event that occurs, 4 metres north of the origin, 5 metres east, 1 metre in the air and 10 seconds in the future.

But why do I say might represent? Why don't I just tell you if it does or it doesn't? Well, a scalar might represent a point on a number line, but it could also represent the angle of the Moon in the sky, or the momentum of a fast train, or any number of things. It depends what you use it for! Likewise, the vector (100, 100, 0) might represent a point in space, but could also represent a color halfway between red (100) and green (100) without any blue (0).

As with scalars, there are an infinite number of uses for vectors, and there are many ways of expressing them on paper.

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