If \(A, B, C\) are vertices of a triangle with position vectors \(\vec{a}, \vec{b}, \vec{c}\) respectively, then find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).
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To remember the ratio, use the mnemonic: \(BD\) is next to side \(AB\), and \(DC\) is next to side \(AC\). So, \(BD/DC = AB/AC\). This is a very common vector application in MHT-CET!