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BC is divided into four equal parts by P, Q and R. The resultant of $\vec{A B}$ and 3 $\vec{A C}$ is

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$\vec{A R}$

$4 \vec{A R}$

$4 \vec{A P}$

$\vec{P Q}$

answer is B.

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Detailed Solution

$\vec{A C} + \vec{C B} = \vec{A B}; \vec{A C} + 4 \vec{C R} = \vec{A B}$

$\vec{A C} + 4 (\vec{A R} - \vec{A C}) = \vec{A B}; 4 \vec{A R} - 3 \vec{A C} = \vec{A B}$

$∴ \vec{A B} + 3 \vec{A C} = 4 \vec{A R}$

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