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If \(\vec{a}=\hat{i}+\hat{j}+\hat{k},\) \(\vec{b}=4\hat{i}-2\hat{j}+3\hat{k}\) and \(\vec{c}=\hat{i}-2\hat{j}+\hat{k}\) then find a vector of magnitude 6 units which is parallel to the vector \(2\vec{a}-\vec{b}+3\vec{c}.\)

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Since the required vector has magnitude 6 units and parallel to \(\vec{r}.\)

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