The position vectors of the vertices A, B, C of a tetrahedron ABCD are \(\hat...

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Question Id : 3919 | Context : NIMCET 2019

The position vectors of the vertices A, B, C of a tetrahedron ABCD are \(\hat{i} + \hat{j} + \hat{k}\), \(\hat{i}\) and \(3\hat{i}\) respectively and the altitude from the vertex D to the opposite face ABC meets the face at E. If the volume of the tetrahedron is \(\dfrac{2\sqrt{2}}{3}\), then the length of DE is: