Question

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

Answer 1

If $\overline{a}=\lambda \overline{b},$ then $\overline{a}$ and $\overline{b}$ are collinear

$-4\overrightarrow{i}+6\overrightarrow{j}-8\overline{k}=2(2\overrightarrow{i}-3\overrightarrow{j}+4\overline{k})$ or

$2\overrightarrow{i}-3\overrightarrow{j}+4\overline{k}=\frac{1}{2}(-4\overrightarrow{i}+6\overrightarrow{i}-8\overline{k})$

Hence they are collinear.