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In page 249 of Kleppner and Kolenkow, An introduction of Classical Mechanics, for the proof of Parallel axis theorem, he writes the vector connecting the axis(z-axis) to mass element is :

$$ \rho_j= x_j \vec{i} + y_j \vec{k}$$

Now, if it is the perpendicular vector connecting the axis to a mass element then why is there $k$ component..?

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  • $\begingroup$ It is a typo (read the rest of the proof). It should have been $y_j \vec{j} $ instead of $y_j \vec{k} $. $\endgroup$
    – Omar Nagib
    Commented Oct 14, 2020 at 17:54
  • $\begingroup$ Nice! post this as an answer and I'll accept it $\endgroup$
    – Brian
    Commented Oct 14, 2020 at 17:59
  • $\begingroup$ @Buraian Do you feel you understand what the parallel axis theorem means/ $\endgroup$
    – Bob D
    Commented Oct 14, 2020 at 22:14
  • $\begingroup$ What I understand: if you want the inertia about some axis, then you can find the inertia of an axis parallel to that and passing through the center of mass, and using this, find the inertia of the original axis in question $\endgroup$
    – Brian
    Commented Oct 15, 2020 at 3:56

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From the comment by Omar Nagib,

It is a typo.

The correction : $y_i \vec{j}$ instead of $yj\vec{k}$

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