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
If  then do you think that A is necessarily equal to C?
Given that,
            Â
Let angle between  be  and that betweenÂ
∴   Â
   Â
        Â
Now,   if  then A = C, and
        thenÂ
Thus A is not necessarily equal to C.
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