In a trapezium \( \mathrm{ABCD}, \mathrm{AB} \| \mathrm{DC} \) and \( \mathrm{DC}=2 \mathrm{AB} ...

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In a trapezium \( \mathrm{ABCD}, \mathrm{AB} \| \mathrm{DC} \) and \( \mathrm{DC}=2 \mathrm{AB} . \mathrm{EF} \) drawn parallel to \( \mathrm{AB} \) cuts \( \mathrm{AD} \) at \( \mathrm{F} \) and \( \mathrm{BC} \) at \( \mathrm{E} \) such that \( \frac{\mathrm{BE}}{\mathrm{EC}}=\frac{3}{4} \). Diagonal \( \mathrm{DB} \) intersects \( \mathrm{FE} \) at \( \mathrm{G} \). Then which of the following is true?
a. \( 7 \mathrm{FE}=5 \mathrm{AB} \)
b. \( 7 \mathrm{EF}=10 \mathrm{AB} \)
c. \( 5 \mathrm{AB}=8 \mathrm{FE} \)
d. \( 5 \mathrm{AB}=8 \mathrm{FE} \)
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