two forces act at 60 degrees and their resultant is 14 neutons, if they act at 90 degrees their resultant is 90 degrees. find the mangitude of forces?

A2A.

Let the magnitude of the two forces be x and y.

Let resultant at right angle be p ( = √15N) and at 60 degrees be q ( = √18N.

Now, p = √ (x2 + y2) = √15,

q = √ (x2 + y2 + 2xycos60) = √18.

So x2 + y2 = 15,

x2 + y2 + xy = 18,

therefore xy = 3 or y = 3/x.

Now, x2 + (3/x) 2 = 15,

x4 + 9 = 15x2,

x4 - 15x2 + 9 = 0.

Now find the roots of this quadratic equation, the two values of x will correspond to the magnitudes of the two vectors.