Resolution of vectors

A vector can be resolved into two component parts such that the vector addition of the component parts is equal to the original vector. The two components usually taken are a horizontal component and a vertical component.
For the vector shown as F in the Figure, the horizontal component of F is Fcosθ and the vertical component is Fsinθ.

the horizontal component of F is Fcosθ and the vertical component is Fsinθ.

Example 1:

Resolve the force vector of 30 Newton at an angle of 35 Degree to the horizontal into a horizontal and a vertical component

Solution

Resolving force vector of 30 Newton at an angle of 35 Degree to the horizontal into a horizontal and a vertical component

  

Example 2:

Resolve the acceleration vector of 17 m/s2 at an angle of 120◦ to the horizontal into a horizontal and a vertical component

Solution

Horizontal component    ,
 acting from left to right.

Vertical component ,
acting vertically upwards.

These component vectors are shown in the Figure: