What is a vector? In introductory physics a vector is a quantity that has a magnitude and a direction.  We use it to represent things like forces, displacements, velocities, and accelerations, as well as other physical quantities.

This is different than scalars, quantities that only have a size.  For example the mass of an object only has a size, measured in kilograms.

A length is a scalar with a particular magnitude.  When we point it in a particular direction, it becomes a displacement, which is a vector.

Representing a vector

A generic displacement vector.Vectors are represented by arrows in our drawings, as seen in the figure.  When you write a vector down, you give it a letter with an arrow drawn on top of it.  For example, a displacement vector would be written as…

\(\color{black}{\vec{d}}\)

A displacement vector tells us which way to go, and how far to go in order to get there.  A treasure map might contain a list of vectors.  For example, walk 10 paces from the rock towards a tree.  Turn left, and then go 5 paces.  We’ll see how to add vectors in a later lesson.

Two ropes and the forces they transmit.If you have two people pulling on ropes connected to an object, you would represent each of the forces with an arrow.  Longer arrows would be used to represent larger forces.  It makes sense to give vectors a label that makes sense.  Here, we used an F because it represents a force.  We give the two subscripts to tell them apart.
We use vectors throughout physics.  It is a good idea to make sure you really understand them early in your physics class.

What is a vector?

The answer to the question “What is a vector?” is this. Vectors are a useful tool to describe any quantity that has a magnitude and a direction. Let’s spend some time learning more about vectors.

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