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At what angle must the two forces (x+y) ...

At what angle must the two forces `(x+y)` and `(x-y)` act so that the resultant may be `sqrt((x^(2)+y^(2)))` :-

A

`cos^(-1) [ (-(x^(2) + y^(2)))/(2(x^(2) -y^(2))]`

B

`cos ^(-1) [(-2( x^(2) -y^(2)))/(x^(2) + y^(2))]`

C

`cos^(-1) [(-(x^(2) + y^(2)))/(x^(2)-y^(2))]`

D

`cos^(-1) [ ((x^(2) -y^(2))/(x^(2) +y^(2))]`

Text Solution

Verified by Experts

The correct Answer is:
1
`(sqrt((x^(2) + y^(2)))^(2)`
`=(sqrt((x+y)^(2) + (x-y)^(2) + 2(x+y)(x-y)costheta))^(2)`
`x^(2) + y^(2) = 2( x^(2) + y^(2)) + 2(x^(2) -y^(2) ) costheta `
`cos theta = - ((x^(2) + y^(2)))/( 2 (x^(2) - y^(2)))`
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