The vectors \( c, a, b \) are such that \( a \cdot b = 2a \cdot c \), \( |c| = 1 \), \( |b| = 4 \), and \( |b \times c| = \sqrt{15} \), if \( b - 2c = \lambda \alpha \), then \( \lambda \) equals:
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When solving vector problems, use the properties of dot and cross products to find relationships between the vectors and solve for unknowns.