Q1. (a) The line elements of R In Cartesian, cylindrical polar and spherical polar coordinates are...

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Q1. (a) The line elements of R³ In Cartesian, cylindrical polar and spherical polar coordinates are Respectively given by: ds² = dx² + dy² + dz², ds² = dp² + p² dp² + dz² ds² = dr² + r²d0² +r² sin²0do² Evaluate guv, gv and g, where g = det(9µv). (b) Evaluate/expand the following V₁(wvgPHV₁) where the quantity in parenthesis is a scalar/inner product. Also prove that V₁(wvgPHVμ) = ₂(w₂g²μVμ) or V₁(w₂V²) = ₂(w₂Vº). Q1. (a) The line elements of R³ In Cartesian, cylindrical polar and spherical polar coordinates are Respectively given by: ds² = dx² + dy² + dz², ds² = dp² + p² dp² + dz² ds² = dr² + r²d0² +r² sin²0do² Evaluate guv, gv and g, where g = det(9µv). (b) Evaluate/expand the following V₁(wvgPHV₁) where the quantity in parenthesis is a scalar/inner product. Also prove that V₁(wvgPHVμ) = ₂(w₂g²μVμ) or V₁(w₂V²) = ₂(w₂Vº).