\(\vec{a}\) and \(\vec{b}\) are non-zero non-collinear vectors such that \(|\vec{a}| = 2\), \(\vec{a}\cdot \vec{b} = 1\) and the angle between \(\vec{a}\) and \(\vec{b}\) is \(\dfrac{\pi}{3}\). If \(\vec{r}\) is any vector satisfying \(\vec{r}\cdot \vec{a} = 2\), \(\vec{r}\cdot \vec{b} = 8\), \((\vec{r} + 2\vec{a} - 10\vec{b})\cdot(\vec{a}\times \vec{b}) = 6\) and \(\vec{r} + 2\vec{a} - 10\vec{b} = \lambda(\vec{a}\times \vec{b})\), then \(\lambda =\)