In scalars, sometimes it is helpful to “break up” a number. For example, 27 is 20 + 7. In vectors we have a similar thing. When we “break up” a vector into two perpendicular components, we are resolving the vector.
As shown above, the tension force T is resolved into its vertical and horizontal components, which have magnitudes Tcosθ and Tsinθ respectively.
As shown above, the vertical weight mg is resolved into its component parallel to the slope mgsinθ and component perpendicular to the slope mgcosθ.
Resolving vectors is actually the reverse of the summation of two perpendicular vectors: instead of finding the resultant vector from the hypotenuse, we are finding the components from the sides of the right-angled triangle. So when sketching your vector diagram to resolve a vector, make sure that the vector to be resolved is the diagonal of the rectangle. The adjacent and opposite sides of the rectangle will then correspond to the two perpendicular components we are looking for.
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Video Explanation
Resolving Vectors: Why is Component of Weight Along Slope mgsinθ?
Concept Test
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