Let A and B be the magnitude of two vectors and let A>B.
When act in opposite direction, the magnitude of resultant is A - B
Now,
A - B = 7 [Given] ...(1)
When act perpendicular to each other, then their resultant is,
...(2)
Now,
∴
and
or ...(3)
On solving equation (1) and (3), we get
A = 12 and B = 5
Let be the velocities of boat and river water respectively.
Let be the resultant velocity of boat.
Boat heads towards north and water current is in the direction east of south.
Therefore, the angle between is
Now using parllelogram law of vector addition, the magnitude of resultant velocity is ,
Let the resultant velocity vector subtend an angle with the north.
Then,
This implies,