Vector Addition and Subtraction

Graphic Methods

Vectors Quantities having both magnitude and

direction are vector quantities. Vectors can be represented by an

arrow-tipped line segment. Examples of vectors:

Velocity Acceleration Displacement Force

Vector Terminology Two or more vectors acting on the same

point are said to be concurrent vectors. The sum of 2 or more vectors is called

the resultant (R). Any vector can be described as having

both x and y components in a coordinate system.

The process of breaking a single vector into its x and y components is called vector resolution.

Using the Graphic Method of Vector Addition:

Vectors are drawn to scale and the resultant is determined using a ruler and protractor.

Vectors are added by drawing the tail of the second vector at the head of the first (tip to tail method). The order of addition does not matter.

The resultant is always drawn from the tail of the first to the head of the last vector.

Any number of vectors can be added using this method.

Example Problem

A 50 N force at 0° acts concurrently with a 20 N force at 90°.

RΘ Θ

R and Θ are equal on each diagram.

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Vector Subtraction The process of vector subtraction

is the same as vector addition. Addition: Subtraction: where -B has

the same magnitude as B but its direction is reversed by 180o.

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Aur

+ Bur

=Rur

Aur

+ −Buru

( ) =Rur

Example Problem:Motion in 2 Dimensions

A boat heads east at 8.00 m/s across a river flowing north at 5.00 m/s. What is the resultant velocity of the

boat?

A boat heads east at 8.00 m/s across a river flowing north at 5.00 m/s.

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