Thu August 25, 2011 By:

Can you please explain the laws of vector addition .

Expert Reply
Thu August 25, 2011
In most of the situations, we are involved with the addition of two vector quantities. Triangle law of vector addition is appropriate to deal with such situation.

If two vectors are represented by two sides of a triangle in sequence, then third closing side of the triangle, in the opposite direction of the sequence, represents the sum (or resultant) of the two vectors in both magnitude and direction.

Here, the term “sequence” means that the vectors are placed such that tail of a vector begins at the arrow head of the vector placed before it.
Parallelogram law, like triangle law, is applicable to two vectors.
If two vectors are represented by two adjacent sides of a parallelogram, then the diagonal of parallelogram through the common point represents the sum of the two vectors in both magnitude and direction.

Parallelogram law, as a matter of fact, is an alternate statement of triangle law of vector addition. A graphic representation of the parallelogram law and its interpretation in terms of the triangle is shown in the figure :
Converting parallelogram sketch to that of triangle law requires shifting vector, b, from the position OB to position AC laterally as shown, while maintaining magnitude and direction.
The polygon law is an extension of earlier two laws of vector addition. It is successive application of triangle law to more than two vectors. A pair of vectors (a, b) is added in accordance with triangle law. The intermediate resultant vector (a + b) is then added to third vector (c) again, successively till all vectors to be added have been exhausted.

If (n-1) numbers of vectors are represented by (n-1) sides of a polygon in sequence, then n-th side, closing the polygon in the opposite direction, represents the sum of the vectors in both magnitude and direction.
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