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)


Cx = Ax + Bx

Cy = Ay + By


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


Cx = Ax + Bx

Cy = Ay + By


Cz = Az + Bz


C = A + B

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

Two dimensional motion with constant acceleration can be handled with vectors. The resulting motion is called projectile motion and the path of an object undergoing such motion is a parabola.

Projectile motion -- motion only under the influence of gravity -- is a combination of

horizontal motion with constant velocity and

vertical motion with constant acceleration.

Uniform Circular Motion (UCM) is another example of non-linear motion. UCM requires an acceleration directed toward the center of the circle. This acceleration is called the centripetal acceleration ("centripetal" means center-seeking). This centripetal acceleration is

ac = v2/r

Unit Vectors


Return to ToC, Vectors and 2D Motion

(c) 2002, Doug Davis; all rights reserved