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A forceF has magnitude of 15N. Direction...

A force`F` has magnitude of `15N`. Direction of `F` is at `37^(@)` from nagative x-axis towards posititve y-axis. Represent F in terms of `hat i` and `hat J` .

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The correct Answer is:
A, B
The given force is as shown in figure. Let us find its x and y components.
`F_x = F cos 37^@`
`=15xx(4)/(5)`
`= 12n ("along negative x-axis")`
`F_y = F sin 37^@`
`=15xx(3)/(5)`
`=9N ("along positive y -axis")`
From parallelogram law of vector addition, we can see that
`F = OM+ON`
`=F_x(-hat i)+F_y(hat J)`
`=(-12hat j) N` .
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