Vector Algebra

If \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are three vectors, \(|\overline{\mathrm{a}}|=2,|\overline{\mathrm{b}}|=4,|\overline{\mathrm{c}}|=1, |\bar{b} \times \bar{c}|=\sqrt{15}\) and \(\bar{b}=2 \bar{c}+\lambda \bar{a}\), then the value of \(\lambda\) is