Given, \(\vec{a}=\hat{i}+4\hat{j}+2\hat{k},\) \(\vec{b}=3\hat{i}-2\hat{j}+7\hat{k},\) \(\vec{c}=2\hat{i}-\hat{j}+4\hat{k}\)
Vector \(\vec{p}\) is perpendicular to both \(\vec{a}\) and \(\vec{b}\) \(i.e,\) \(\vec{p}\) is parallel to vector \(\vec{a}\,\times \vec{b}.\)
Since \(\vec{p}\) is parallel to \(\vec{a}\,\times \vec{b}\)