Trigonometric EquationHard

Question

The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N. The magnitude of the two forces are

Options

A.13, 5
B.12, 6
C.14, 4
D.11, 7

Solution

         
Let two forces be P and Q. Given P + Q = 18 and
⇒ P2 + 144 = Q2 = (18-P)2; ⇒ P2 + 144 = 324 - 36P + P2
⇒ 36P = 180 ⇒ P = 5 and Q = 13
(where and are unit vectors along P and Q).

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