Unit 2 - Objective 2 - Components of Vectors
Quick Review

Graphical decomposition of a single vector to produce two vectors whose sum is the original vector (resolving the vector into its components):


'c' is the original vector
'a' and 'b' are the components of 'c'

The above set into the XY coordinate plane:


'b' is the component of 'c' in the X-direction
'a' is the component of 'c' in the Y-direction


By definition:




Note that is in standard position
(measured with respect to the positive x-axis)

Fy = F SIN       Fx = F COS



Examples

1) Resolve a vector 12.0 units long at an angle of 150° into its horizontal and vertical components.

One component is along the negative x-axis and has an approximate magnitude of 10.4 units. The other component is along the positive y-axis and has a magnitude of 6.0 units.

2) Resolve this vector:


The components would be:


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