If&nbsp;<span class="math-tex">\(\vec a\)</span>&nbsp;and&nbsp;<span class="math-tex">\(\vec b\)</span>&nbsp;are vectors in space, given by&nbsp;<span class="math-tex">\(\vec a = \frac {\hat i - 2\hat j}{\sqrt 5}\)</span>&nbsp;and&nbsp;<span class="math-tex">\(\vec b = \frac {2\hat i + \hat j + 3\hat k}{\sqrt {14}}\)</span>&nbsp;then the value of&nbsp;<span class="math-tex">\(\left(2\vec a + \vec b\right)\left[\left(\vec a \times \vec b\right)\times \left(\vec a - 2\vec b\right)\right]\)</span>&nbsp;is