The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at `90^(@)` with the force of smaller magnitude, What are the magnitudes of forces?

Options

A. 5, 13
B. 6, 12
C. 7, 11
D. 8, 10

Answer

A

Explanation

`A+B=18`
`sqrt(A^(2)B^(2)+2AB cos theta)=12`
`A+B cos theta=0`
`A^(2)+B^(2)-2A^(2)=144`
`(B+A)(B-A)=144`
`B-A=(144)/(18)=8 " " A=5" " B=13`