Let \( A, B, C, D, E \) represent vertices of a regular pentagon \(...

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Let \( A, B, C, D, E \) represent vertices of a regular pentagon \( A B C D E \). Given the position vector of these vertices be \( \vec{a}, \vec{a}+\vec{b}, \vec{b}, \lambda \vec{a} \) and \( \lambda \vec{b} \), respectively.
\( \mathrm{P} \) \( A D \) divides \( E C \) in the ratio
(1) \( \cos \frac{2 \pi}{5}: 1 \)
(2) \( \cos \frac{3 \pi}{5}: 1 \)
(3) \( 1: 2 \cos \frac{2 \pi}{5} \)
(4) \( 1: 2 \)
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