Prove that:
, where  is the angle betweenÂ
By using distributive and commutative law, the dot product can be evaluated as,Â
 Â
  Â
Â
         Â
That is,
    Â
Find a vector having magnitude equal to the magnitude of vector  and parallel to vectorÂ
Magnitude of vector A is,
  Â
Unit vector in direction of vectorÂ
The vector that has magnitude same as that of vector and parallel to vectorÂ
   Â
Find the unit vector along the resultant ofÂ
Resultant of  is
Â
∴  Unit vector in direction ofÂ
If  and angle between  is twice the angle between  then show that  where  is the angle betweenÂ
It is given that angle between  is Â
Therefore the angle between  will beÂ
Here, Â Â Â Â
∴     Â
       Â
         .
Hence proved.Â