The position vector of the point which divides the join of points $2 \vec{a}-3 \vec{b}$ and $\vec{a}+\vec{b}$ in the ratio $3: 1$ is
(A) $\frac{3 \vec{a}-2 \vec{b}}{2}$
(B) $\frac{7 \vec{a}-8 \vec{b}}{4}$
(C) $\frac{3 \vec{a}}{4}$
(D) $\frac{5 \vec{a}}{4}$
The correct option is (D).
The given vectors are in the ratio 3: 1
Sor the
position vector of the required point $c$ which divides the join of the given vectors $\vec{a}$ and $\vec{b}$ is
$\vec{c}=\frac{m_{1} x_{2}+m_{2} x_{1}}{m_{1}+m_{2}}$
$-\frac{1-(2 \vec{a}-3 \vec{b})+3(\vec{a}+\vec{b})}{3+1}=\frac{2 \vec{a}-3 \vec{b}+3 \vec{a}+3 \vec{b}}{4}$
$=\frac{5 \vec{a}}{4}=\frac{5}{4} \vec{n}$
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