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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) [-(-2x^(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:
A
(a) Resultant `A^(2)=A^(2)+B^(2)+2ABcostheta`
`"substiting",A=(x+y),B=(x-y)`
`and R=sqrt(x^(2)+y^(2))`
`We get theta =cos^(-1) [-((x^(2)+y^(2)))/(2(x^(2)-y^(2)))]`
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