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Answer :
In \( \triangle ABC\), given as, DE || AC
Thus, by using Basic Proportionality Theorem, we get,
\(\frac{BD}{DA} = \frac{BE}{EC}\) ………………………………………………(i)
In \( \triangle ABC\), given as, DF || AE
Thus, by using Basic Proportionality Theorem, we get,
\(\frac{BD}{DA} = \frac{BF}{FE}\) ………………………………………………(ii)
From equation (i) and (ii), we get
\(\frac{BE}{EC} = \frac{BF}{FE}\)
Hence, proved.