Question

If \(\vec{a} = \hat{i} + \hat{j} + \hat{k},\; \vec{b} = 2\hat{i} - \hat{j} + 3\hat{k}\) and  \(\vec{c} = \hat{i} - 2\hat{j} + \hat{k} \) find a unit vector parallel to the vector \(2\vec{a} - \vec{b} + 3\vec{c}\)

Answer 1

\(2\vec{a} - \vec{b} + 3\vec{c} = 3\vec{i} - 3\vec{j} + 2\vec{k}\)