Question

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

Answer 1

Let $\overrightarrow{a}=2\hat{i}-3\hat{j}+4\hat{k}$

And, $\overrightarrow{b}=-4\hat{i}+6\hat{j}-8\hat{k}$

By observation, $\overrightarrow{b}=-2(2\hat{i}-3\hat{j}+4\hat{k})=-2\overrightarrow{a}$

Therefore,

$\overrightarrow{b}=\lambda \overrightarrow{a}$, where $\lambda =-2$

Hence, the given vectors are collinear.