The vectors \(\vec{a}\)= (2\(\hat{i}\) -3\(\hat{j}\)+ 4\(\hat{k}\)) and \(\vec{b}\)= (-4\(\hat{i}\) + 6\(\hat{j}\)- 8\(\hat{k}\)) are-

Collinear

We have \(\vec{a}\)= (2\(\hat{i}\) -3\(\hat{j}\)+ 4\(\hat{k}\)) and \(\vec{b}\)= (-4\(\hat{i}\) + 6\(\hat{j}\)- 8\(\hat{k}\))

It is observed that  \(\vec{b}\)= (-4\(\hat{i}\) + 6\(\hat{j}\)- 8\(\hat{k}\))  = -2 (2 \(\hat{i}\) -3\(\hat{j}\)+ 4\(\hat{k}\)) = -2  \(\vec{a}\)

                              \(\vec{b}\)  = λ  \(\vec{a}\)

                            where λ = -2

Hence, the given vectors are collinear.