Can someone please explain this type of vector to me, I can not understand it.

  • Axial vectors have an inner orientation, i.e. the direction of the vector indicates the positive orientation. For example, a unit linear force vector: the positive direction of the force does not depend on the orientation (right-handed vs. left-handed) of the world reference frame. As many (but not all) other textbooks, this book implicitly uses right-handed reference frames only, but no physical arguments prevent the use of left-handed frames.

  • Polar vectors have an outer orientation, i.e. the positive orientation cannot be derived from the direction vector itself, but is imposed on it by the environment." For example, a unit moment of force vector: if the handedness of the world frame changes, the orientation associated with the moment vector changes too. Note that this is a feature of the coordinate representation, not of the physical property that the vector stands for.

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    $\begingroup$ I suspect the more common names for what you call "axial vector" and "polar vector" are "pseudovector" and "vector". See this answer of mine for another explanation of the difference between them. $\endgroup$ – ACuriousMind Apr 19 at 20:51
  • $\begingroup$ Possible duplicate. At least worth reading the answers therein. $\endgroup$ – jacob1729 Apr 19 at 21:07

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