Two forces are such that the sum of thier is 18 N magnitude of the resultant is 12 N and thier resultant is perpendicular to the smaller force then the magnitude of the product vector A ( Vector B× vector A) is-
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let the smaller force be B, the larger force be A, resultant being C.
Given : |A| + |B| = 18, |C| = 12
A,B,C simply form a right angle triangle with base B vector ,hypotenus being A
So, you have one equation with you : A + B = 18
so simply solving both equations
= A - B = 8 and
= A + B = 18
add both
2a = 26
A = 13
B = 5
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