The resultant of two vectors  is  and perpendicular to  Show thatÂ
Let the angle between  and  beÂ
Resultant of  is A.
Therefore,
         Â
      Â
      Â
              ...(1)
Also resultant is perpendicular toÂ
∴       Â
                          ...(2)
From (1) and (2)
        Â
     Â
The magnitude of the resultant of  is P; If direction of  is reversed, the resultant is Q.
Show that
       Â
Let  be the  angle between two vectorsÂ
∴           ...(1)
If direction of  is reversed then, then angle between  becomesÂ
∴       .
             ...(2)
Adding (1) and (2), we get
       Â
If  and  then what is the angle betweenÂ
Let  be the angle between Â
∴ Resultant is given by,
Â
Â
Hence, R = A = B
Thus, Â
  Â
 Â
    , is the required angle between them.Â