If `x=rsinthetacosvarphi` , `y=rsinthetasinvarphi` and `z=rcostheta` , then (a)`x^2+y^2+z^2=r^2` (b) `x^2+y^2-z^2=r^2` (c) `x^2-y^2+z^2=r^2` (d) `z^2+y^2-x^2=r^2`

If x=r sin theta cos varphi,y=r sin theta sin varphi and z=r cos theta, then x^(2)+y^(2)+z^(2)=r^(2)(b)x^(2)+y^(2)-z^(2)=r^(2)(c)x^(2)-y^(2)+z^(2)=r^(2)(d)z^(2)+y^(2)-x^(2)=r^(2)

If x=rcos thetacosphi,y=rcosthetasinphi and z=r sin theta, show that , x^2+y^2+z^2=r^2

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

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

Locus of the point (r sec alpha cos beta,r sec alpha sin beta,r tan alpha) is (a). x^(2)-y^(2)-z^(2)=r^(2) (b). x^(2)-y^(2)+z^(2)=r^(2) (c). x^(2)+y^(2)+z^(2)=r^(2) (d) . x^(2)+y^(2)-z^(2)=r^(2)

If x=rsinAcosC ,\ \ y=rsinAsinC and z=rcosA , prove that r^2=x^2+y^2+z^2

If x=rsinAcosC ,\ \ y=rsinAsinC and z=rcosA , prove that r^2=x^2+y^2+z^2

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n (a) x^2+y^2+z^2+x y z=0 (b) x^2+y^2+z^2+2x y z=0 (c) x^2+y^2+z^2+x y z=1 (d) x^2+y^2+z^2+2x y z=1

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n (a) x^2+y^2+z^2+x y z=0 (b) x^2+y^2+z^2+2x y z=0 (c) x^2+y^2+z^2+x y z=1 (d) x^2+y^2+z^2+2x y z=1