If vec{a}, vec{b}, vec{c}, vec{d} are positio | vedclass

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(D) Given the equation: $2 \vec{a} + 3 \vec{b} + 5 \vec{c} - 10 \vec{d} = \vec{0}$.Rearranging the terms to isolate the vectors $\vec{a}, \vec{b}$ on

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$3:2$

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(D) Given the equation: $2 \vec{a} + 3 \vec{b} + 5 \vec{c} - 10 \vec{d} = \vec{0}$.Rearranging the terms to isolate the vectors $\vec{a}, \vec{b}$ on one side and $\vec{c}, \vec{d}$ on the other:$2 \vec{a} + 3 \vec{b} = 10 \vec{d} - 5 \vec{c}$.Divide both sides by $5$:$\frac{2 \vec{a} + 3 \vec{b}}{5} = 2 \vec{d} - \vec{c}$.We can rewrite the left side as a section formula form $\frac{m \vec{b} + n \vec{a}}{m+n}$:$\frac{3 \vec{b} + 2 \vec{a}}{3+2} = \frac{2 \vec{d} - \vec{c}}{2-1}$.This represents a point $P$ that lies on the line segment $AB$ and also on the line $CD$.The point $P$ divides the segment $AB$ in the ratio $3:2$ internally.Thus,the line joining $\vec{c}$ and $\vec{d}$ divides the line segment joining $\vec{a}$ and $\vec{b}$ in the ratio $3:2$.

If $\vec{a}, \vec{b}, \vec{c}, \vec{d}$ are position vectors of $4$ points such that $2 \vec{a}+3 \vec{b}+5 \vec{c}-10 \vec{d}=\vec{0}$,then the ratio in which the line joining $\vec{c}$ and $\vec{d}$ divides the line segment joining $\vec{a}$ and $\vec{b}$ is

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