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