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The unit vectors of the cylindrical and spherical systems differ from the Cartesian ones in that they

  • A.have magnitudes that vary with position in space
  • B.cannot be used to express a vector in component form
  • C.change direction from point to point
  • D.are not mutually perpendicular at a general point in space

Answer: C

The radial unit vector points away from the axis or origin, so it points differently at different places. This is why they cannot simply be moved outside a derivative or an integral, and why gradient, divergence and curl take different forms in each system.

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