Vector Addition

Adding Multiple Vectors by Drawing

To add vectors you place the base of the second vector on the tip of the first vector

You make a path out of the arrows like you’re drawing a treasure map

The answer vector (called the resultant) is the vector that connects the start of the path to the end of the path.

Measure the resultant with a ruler to find the magnitude.

Add These Vectors by Drawing

3 cm @ 90° + 6 cm @ 0° = ?

resultant (answer vector)

Tip-to-Tail

This method of adding vectors is called the “Tip-to-tail method” since you put the tail of the second vector on the tip of the first vector

resultant (answer vector)

Adding Vectors Mathematically When adding perpendicular vectors

you use the Pythagorean Theorem

a

bc

Finding the Direction

When adding vectors by drawing you use a protractor and measure the angle of the resultant.

When adding vectors mathematically you use Trigonometry to find the direction of the resultant.

Trig Functions

Sine (sin) Cosine (cos) Tangent (tan) Each function uses two sides of a

right triangle The angle we are using is labeled with

the Greek letter “theta” or “θ”

SOH-CAH-TOA

θ

hypotenuse

op

posi

te

adjacent

Angles

Angles are measured from the +x-axis

Quadrant 1: 0°-90°Quadrant 2: 90°-180°

Quadrant 3: 180°-270° Quadrant 4: 270°-360°

Your calculator will give you the angle

to the closest part of the x-axis. You need to add or subtract to adjust the angle to the ranges shown.

y

x

Example: MagnitudeA hiker hikes 22 km East, then 11 km North. Determine the magnitude and direction of the hiker’s displacement.

θ

22 km

11 kmresultant

Example: DirectionA hiker hikes 11 km East, then 22 km North. Determine the magnitude and direction of the hiker’s displacement.

θ

22 km

11 kmresultant

Your calculator must be in degrees mode!