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.
Proof: Let us consider that three vectors
are represented by
Let, the angle between
and that between
In the fig. above, the resultant vector is given by
is the resultant of
Angle made by
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.