Resultant of Two Forces Using Vectors
To find the resultant of two forces acting at a point, construct a parallelogram with the forces as the sides of the parallelogram. The resultant will be a diagonal of the parallelogram.
Example: Find the resultant of the two forces illustrated in the diagram.
![resultant of two forces](/a-level-maths/M1/forces-11.png)
First construct the parallelogram.
![resultant of two forces](/a-level-maths/M1/forces-22.png)
The resultant is the diagonal shown. ![resultant of two forces](/a-level-maths/M1/forces-33.png)
We can find the diagonal using the Cosine Rule. We get
\[R^2=35^2+45^2-2 \times 35 \times 45 \times cos140^o=6063 \]
\[R=77.87N\]
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