If a and b are the position vectors of A and | vedclass

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(D) Given that $\overrightarrow{AC} = 3\overrightarrow{AB}$.Let $\vec{a}$ and $\vec{b}$ be the position vectors of points $A$ and $B$ respectively.We

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$3b - 2a$

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(D) Given that $\overrightarrow{AC} = 3\overrightarrow{AB}$.Let $\vec{a}$ and $\vec{b}$ be the position vectors of points $A$ and $B$ respectively.We know that $\overrightarrow{AB} = \vec{b} - \vec{a}$.Substituting this into the given equation:$\overrightarrow{AC} = 3(\vec{b} - \vec{a}) = 3\vec{b} - 3\vec{a}$.Let $\vec{c}$ be the position vector of point $C$. Then $\overrightarrow{AC} = \vec{c} - \vec{a}$.Equating the two expressions for $\overrightarrow{AC}$:$\vec{c} - \vec{a} = 3\vec{b} - 3\vec{a}$.$\vec{c} = 3\vec{b} - 3\vec{a} + \vec{a}$.$\vec{c} = 3\vec{b} - 2\vec{a}$.Thus,the position vector of point $C$ is $3\vec{b} - 2\vec{a}$.

If $a$ and $b$ are the position vectors of $A$ and $B$ respectively,then the position vector of a point $C$ on $AB$ produced such that $\overrightarrow{AC} = 3\overrightarrow{AB}$ is

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