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.
Solution:
Let $\vec{a}=2 \hat{i}-3 \hat{j}+4 \hat{k}$ and $\vec{b}=-4 \hat{i}+6 \hat{j}-8 \hat{k}$.
It is observed that $\vec{b}=-4 \hat{i}+6 \hat{j}-8 \hat{k}=-2(2 \hat{i}-3 \hat{j}+4 \hat{k})=-2 \vec{a}$
$\therefore \vec{b}=\lambda \vec{a}$
where,
$\lambda=-2$
Hence, the given vectors are collinear.
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