Vector Resolution (Component Vector Resolution (Component Method) Method)

of Finding the Resultantof Finding the Resultant

The vector resolution (component The vector resolution (component method) can be used to find the resultant method) can be used to find the resultant in any situation, no matter the vectors’ in any situation, no matter the vectors’ orientation, or the number of vectors orientation, or the number of vectors involved.involved.

A=A, θA

B=B, θB

C=C, θCAθ

Bθ

Cθ AA

B

C

Ax

Ay

A

B

Bx

By

Cx

Cy

Each vector can be broken down into components.

Ax = A cos θA

Ay = A sin θA

Bx = B cos θB

By = B sin θB

Cx = C cos θC

Cy = C sin θC

A=(Ax)x+(Ay)y

B=(Bx)x+(By)y

C=(Cx)x+(Cy)y

Honors:Component form:

Ax

Ay

Bx

By

Cx

Cy

Rx=Ax+Bx+Cx

Ry=Ay+By+Cy

The resultant horizontal magnitude can be found by adding all of the x components.

The resultant vertical magnitude can be found by adding all of the y components.

Ry

Rx

R=(Rx)x+(Ry)y

Honors:

(component form)

Rx

Ry

R

2y

2x )R()(RR

θ

θ R,R

The resultant can be obtained by adding the horizontal and vertical components of the resultant.

Adjust angle if necessary.

x

y1-

R

Rtan

Find the angle when:Find the angle when:

RRxx= -1= -1

RRyy= +1= +1

45

1

1tan

R

Rtan 1

x

y1- 135°

45

1

1tan

R

Rtan 1

x

y1- 225°

(2nd quadrant)

(3rd quadrant)

Rx=-1Ry=-1

The correct quadrant must be double-checked.

1st quadrant (0° to 90°):Rx= +Ry= +

2nd quadrant (90° to 180°):Rx=-Ry+

3rd quadrant (180° to 270°):Rx= -Ry=-

4th quadrant (270° to 360°):Rx=+Ry=-

Rx

Ry

R

Rx

Ry

R

R

R

Rx

Rx

Ry

Ry