Question
State and prove that dot product is distributive.
Solution
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 
.
Angle made by
.
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 . 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.
