If $\Large\frac{1}{a},\frac{1}{b},\frac{1}{c}$are the $\large p^{th},q^{th}and\;r^{th}\;$ terms of an AP and $\bar{u}=(q-r)\bar{i}+(r-p)\bar{j}+(p-q)\bar{k}\;and\;\bar{v}=\large\frac{1}{a}\bar{i}+\frac{1}{b}\bar{j}+\frac{1}{c}\bar{k}$ then prove that $\bar{u}\; and\;\bar{v}$ are orthogonal vectors.

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