﻿ State and prove associative law for vector addition. from Physics Motion in A Plane Class 11 Manipur Board

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State and prove associative law for vector addition.

The associative law of vector states that the vector addition is same, in whatever grouping they are added.

Proof:

Let there be three vectors . These three vectors, both magnitude and direction are represented by three vectors  of polygon OLKG.

Now, using polygon law of vector addition, the resultant of the vector will be represented by the closing side of the polygon
Join O with K, L and G.

Now, applying triangle law to , we have

Now, in , we have

Now, applying the triangle law of vector addition to we have

For triangle OLG, we get

Now, from equations (1) and (2), we get

Therefore, the vector addition is assosciative.

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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
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