Vector Algebra

Let a, b, c be three vector such that \(a \neq 0\) and \(\vec{a} \times \vec{b}=2 \vec{a} \times \vec{c},|a|=|c|=1,|b|=4\) and \(|\vec{b} \times \vec{c}|=\sqrt{15}\). If \(\vec{b}-2 \vec{c}=\lambda \vec{a}\) then \(\lambda\) equals to