what are the differences between polygon and parallelogram method?
The Polygon method and the Parallelogram method are two different methods used to find the resultant of two vectors. Here's a breakdown of the differences between these two methods:
1. Polygon Method:
- In this method, the vectors are drawn as arrows in a plane, one after the other, so that the tail of each vector is placed at the head of the previous vector.
- The resultant vector is then drawn from the tail of the first vector to the head of the last vector.
- The length and direction of the resultant vector can be measured directly from the diagram.
2. Parallelogram Method:
- In this method, the vectors are drawn as arrows in a plane, with their tails at the same point.
- A parallelogram is constructed by drawing lines parallel to the vectors from their heads.
- The diagonal of the parallelogram, starting from the same point as the vectors' tails, represents the resultant vector.
- The length and direction of the resultant vector can be measured directly from the parallelogram.
To actually find the numerical values of the resultant vector using these methods, you need to know the magnitudes and directions of the individual vectors involved. Simple trigonometry can be used to find the magnitudes and angles of the vectors.
In summary, while both the Polygon and Parallelogram methods are used to find the resultant vector, the Polygon method involves placing the vectors end-to-end and measuring the resultant directly, while the Parallelogram method involves constructing a parallelogram and measuring the resultant from its diagonal.