If \( a, b \) are the position vectors of \( A \) and \( B \) respectively, show that the positi...

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If \( a, b \) are the position vectors of \( A \) and \( B \) respectively, show that the position vectors of points \( C \) on the line \( A B \) is such that \( \overrightarrow{A C}=3 \overrightarrow{A B} \) is \( 3 \vec{b}-2 \vec{a} \).
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