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If \(\vec{a},\vec{b},\vec{c}\) are three vectors such that \(|\vec{a}|=5, |\vec{b}|=12\) and \(|\vec{c}|=13,\) and \(\vec{a}+\vec{b}+\vec{c}\) then find the value of \(\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}.\)

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Similarly taking dot product of both sides of (i) by \(\vec{b}\) and \(\vec{c}\) respectively, we get

Adding (ii), (iii) and (iv), we get

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