Show that the vectors 2i-3j+4k and -4i+6j-8k are collinear. - Vidyadip

Question

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

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Answer

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

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