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

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: