﻿ State and prove that dot product is distributive. from Physics Motion in A Plane Class 11 Manipur Board

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State and prove that dot product is distributive.

Dot product is distributive. Dot product of a given vector with a sum of number of other vectors is equal to the sum of the dot product of given vector with the other vectors separately.

That is,

Proof: Let us consider that three vectors  are represented by respectively.

Let, the angle between  is  and that between

In the fig. above, the resultant vector is given by  is the resultant of

Construction: From P and T draw perpendiculars PM and TN on OL and draw perpendicular PS from P on TN.

Hence, from the above result we can see that the dot product is distributive.

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