Parallelogram Law of Vectors

Parallelogram Law of Vectors  states that when the adjacent sides of a parallelogram represent the magnitude and direction of two vectors, the resultants of the two vectors is represented in magnitude and direction by the diagonal of the parallelogram drawn from the common point.

See fig 1 above

When two vectors are inclined to each other, the resultant cannot be obtained by either addition or subtraction of the two vectors but by using the above stated Parallelogram law of vectors.

Example.

A man travel distance A=20km and then another distance B=30km what is the displacement if :

1. A and B are at 90 degree to each other.
2. A towards North and B at N60E
3. A towards west and B at N30E

Solution 

1  See fig 2 above

The direction is the angle which R makes with B

  2. See fig 3

The direction can be obtained by using the sine formula

The direction relative to B

3  See Fig 4

The direction can be obtained by using the sine formula

The direction relative to B

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