Question

Show that the vectors $2\hat{i}-3\hat{j}+4\hat{k}$ and $-4\hat{i}+6\hat{k}-8\hat{k}$ are collinear.

Answer 1

Let $\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}$and $\vec{b}=-4\hat{i}+6\hat{k}-8\hat{k}$.
It is observed that \vec{b}=-4\hat{i}+6\hat{k}-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.