First slide

Vectors

Question

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

Difficult

A

$\vec{A R}$
B

$4 \vec{A R}$
C

$4 \vec{A P}$
D

$\vec{P Q}$

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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