Question

A resultant of two vectors makes 30 degree with one vector and 45 with the other.find the two vectors if the resultant has the magnitude 15.

Answer 1

Let the resultant vector, R be reference vector.
R=20 at an angle of 0 degree.
R is made up of two components, A and B.
A = 20sqrt(3) at an angle of 30 degree.
B is unknown.
R= A + B
Hence, B = R - A
B= 20 - 20sqrt(3) at 30 degree = 20 at -120 degree.

So, the magnitude of other force is 20N and it is making an angle of -120degree with the resultant force.