Vector addition - Solved problem

A force of 4N is included at an angle of 45 degree to a second force of 7 N, both forces acting at a point.
Find the magnitude of the resultant of these two forces and the direction of the resultant with respect to the 7N force by both the ‘triangle’ and the ‘parallelogram’ methods.

Solution

The forces are shown in the Fig (a). Although the 7N force is shown as a horizontal line, it could have been drawn in any direction.

 nose-to-tail method - Fig b

Using the ‘nose-to-tail’ method, a line 7 units long is drawn horizontally to give vector oa in Fig. (b).
To the nose of this vector ar is drawn 4 units long at an angle of 45 degree to oa. The resultant of vector addition is or and by measurement is 10.2 units long and at an angle of 16◦ to the 7N force.


parallelogram method - Fig c

Figure (c) uses the ‘parallelogram’ method in which lines are drawn parallel to the 7N and 4N forces from the noses of the 4N and 7N forces, respectively.
These intersect at R. Vector OR gives the magnitude and direction of the resultant of vector addition and as obtained by the ‘nose-to-tail’ method is 10.2 units long at an angle of 16 degree to the 7N force.