# Summary

Most things we encounter in Physics are either scalars or vectors.

## A scalar quantity has only magnitude and no direction.

This means we can fully explain a scalar with a number and a unit.

## A vector quantity has both magnitude and direction.

The distinction between scalars and vectors is important. We will use bold face type to indicate a vector, such as r. In writing a vector by hand, we will indicate a quantity is a vector by drawing an arrow above it as . Some such distinguising notation is important. Do not write a vector without some distinguishing characteristic or notation.

Consider adding two vectors together as in A + B = C. Each vector can first be resolved into its respective components,

A = (Ax , Ay , Az)

B = (Bx , By , Bz)

The components are then added as the scalars they are and the new vector sum is reconstructed,

C = (Cx , Cy , Cz)

where

Cx = Ax + Bx

Cy = Ay + By

and

Cz = Az + Bz

We will often write this using unit vector notation as

A = Ax i + Ay j + Az k

B = Bx i + By j + Bz k

C = Cx i + Cy j + Cz k

where

Cx = Ax + Bx

Cy = Ay + By

and

Cz = Az + Bz

or

C = A + B

C = (Ax + Bx) i + (Ay + By) j + (Az + Bz) k

Vectors can also be added graphically. A graphical vector addition diagram is an important check on any numerical vector addition.