Question
If $a$, $b$, and $c$ are the $p$th, $q$th, and $r$th terms of a Harmonic Progression (HP), then the vectors $\vec{u} = a^{-1}\hat{i} + b^{-1}\hat{j} + c^{-1}\hat{k}$ and $\vec{v} = (q - r)\hat{i} + (r - p)\hat{j} + (p - q)\hat{k}$:
If $a$, $b$, and $c$ are the $p$th, $q$th, and $r$th terms of a Harmonic Progression (HP), then the vectors $\vec{u} = a^{-1}\hat{i} + b^{-1}\hat{j} + c^{-1}\hat{k}$ and $\vec{v} = (q - r)\hat{i} + (r - p)\hat{j} + (p - q)\hat{k}$: