If \( a, b, c \) are the \( \mathrm{p}^{\text {th }}, \mathrm{q}^{\text {th }}, \mathrm{r}^{\tex...

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If \( a, b, c \) are the \( \mathrm{p}^{\text {th }}, \mathrm{q}^{\text {th }}, \mathrm{r}^{\text {th }} \) terms of an \( \mathrm{HP} \) and \( u=(q-r) i+(r-b) j+(p-q) k \) and \( \vec{v}=\frac{\hat{i}}{a}+\frac{\hat{j}}{b}+\frac{\hat{k}}{c} \) such that \( m=|(\vec{u} \cdot \vec{v})+2| \) find the value of \( (m+4) \).
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