<span class="math-tex">\(\vec a\)</span> and <span class="math-tex">\(\vec b\)</span> are non-zero non-collinear vectors such that <span class="math-tex">\(|\vec a| = 2, \vec a.\vec b = 1\)</span> and the angle between <span class="math-tex">\(\vec a\)</span> and <span class="math-tex">\(\vec b\)</span> is <span class="math-tex">\(\frac \pi 3\)</span>. If <span class="math-tex">\(\vec r\)</span> is any vector satisfying <span class="math-tex">\(\vec r.\vec a = 2,\;\vec r.\vec b = 8,\;(\vec r + 2\vec a - 10\vec b).(\vec a \times \vec b) = 6\)</span> and <span class="math-tex">\(\vec r + 2\vec a - 10 \vec b = λ(\vec a \times \vec b),\)</span> then λ =
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