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

Two vectors area $\overrightarrow{a}=2\hat{i}-3\hat{j}+4\hat{k}$ and $-4\hat{i}+6\hat{j}-8\hat{k}=\overrightarrow{b}$

Now two vectors are collinear, if one vector can be written as other vector.

Here $-2\overrightarrow{a}=\overrightarrow{b}$

$\therefore \overrightarrow{a}$ and $\overrightarrow{b}$ are collinear.