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
If are orthogonal , then prove that
Magnitude of resultant of two vectors acting at angle is given by,
Here, are orthogonal, therefore
Therefore,
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.