Find the magnitude of the two forces, Such that if they act a right angle their resultant is √10 N . But if they act at 60° , their resultant is √13
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Let the magnitude of one vector be A and the other be B.
Thus,
√ A^2 + B^2 + 2ABcos 90° = √10
A^2 + B^2 = 10......(1)
And,
√A^2 + B^2 +2ABcos60° = √13
A^2 + B^2 + AB = 13
AB = 13-10 = 3
Thus,
A = 3/B
Putting this in equation 1
9/B^2 + B^2 = 10
9+B^4 - 10B^2 = 0
(B^2 -9)(B^2 - 1) = 0
B = 3 or B = 1
and thus, A = 3/3 = 1 and A = 3/1 = 3
Thus , two pair of vectors can be made by the following condition where either A is 3 and B is 1 or A is 1 and B is 3.
Thus,
√ A^2 + B^2 + 2ABcos 90° = √10
A^2 + B^2 = 10......(1)
And,
√A^2 + B^2 +2ABcos60° = √13
A^2 + B^2 + AB = 13
AB = 13-10 = 3
Thus,
A = 3/B
Putting this in equation 1
9/B^2 + B^2 = 10
9+B^4 - 10B^2 = 0
(B^2 -9)(B^2 - 1) = 0
B = 3 or B = 1
and thus, A = 3/3 = 1 and A = 3/1 = 3
Thus , two pair of vectors can be made by the following condition where either A is 3 and B is 1 or A is 1 and B is 3.
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