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Answer:
Let the magnitude of smaller force is P, the magnitude of larger force is Q and the resultant force is R.
As the resultant force makes 90∘ with the smaller force P then Q forms the hypotenuse of the triangle.
Thus, it can be written as,
Q² − P² = R²
Q² − P² = (12)²
Q² − P² = 144 Equation 1
The sum of magnitudes of two forces is given as,
P + Q = 18
Q = 18 − P Equation 2
Substituting the value from equation (2) in equation (1), we get
(18−P)² − P²= 144
P = 5N
Substituting the value of P in equation (1), we get
Q = 18 − 5
=13N
Thus, the magnitude of the forces are 5N and 13N.
I understood the concept from toppr and then instead of writing, I copied from them so as to prevent my fingers from paining.