1.

If `x=rsinthetacosphi,y=rsinthetasinphi and z=rcostheta, then x^2+y^2+z^2`is independent of`theta,phi`(b) `r ,theta`(c) `r ,phi`(d) r

Answer» `x = rsinthetacosphi, y = rsinthetasinphi, z = rcostheta`
`:. x^2+y^+z^2 = r^2(sin^2thetacos^2phi+sin^2thetasin^2phi+cos^2theta)`
`=r^2(sin^2theta(1-sin^2phi)+sin^2thetasin^2phi+cos^2theta)`
`=r^2(sin^2theta-sin^2thetasin^2phi+sin^2thetasin^2phi+cos^2theta)`
`=r^2(sin^2theta+cos^2theta)`
`=r^2*1 = r^2`
`:. x^2+y^+z^2 = = r^2`
So, ` x^2+y^2+z^2` is independent of `theta,phi.`


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