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

A=A, θ A B=B, θ B C=C, θ C A A B C

AxAx AyAy A B BxBx ByBy CxCx CyCy Each vector can be broken down into components. A x = A cos θ A A y = A sin θ A B x = B cos θ B B y = B sin θ B C x = C cos θ C C y = C sin θ C A=(A x )x+(A y )y B=(B x )x+(B y )y C=(C x )x+(C y )y Honors: Component form:

AxAx AyAy BxBx ByBy CxCx CyCy 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=(R x )x+(R y )y Honors: (component form)

Rx Ry R The resultant can be obtained by adding the horizontal and vertical components of the resultant. Adjust angle if necessary.

Find the angle when: R x = -1 R y = ° 225° (2 nd quadrant) (3rd quadrant) R x =-1 R y =-1

The correct quadrant must be double-checked. 1 st quadrant (0° to 90°): Rx= + Ry= + 2 nd quadrant (90° to 180°): Rx=- Ry+ 3 rd quadrant (180° to 270°): Rx= - Ry=- 4 th quadrant (270° to 360°): Rx=+ Ry=- Rx Ry R Rx Ry R R R Rx Ry