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

Given, vectors are:

$\overrightarrow{A}=2\hat{i}-3\hat{j}+4\hat{k}and\overrightarrow{B}=-4\hat{i}+6\hat{j}-8\hat{k}$

two vectors $\overrightarrow{A}and\overrightarrow{B}$ are colinear if we can find the value of $n$ such that:

$\overrightarrow{A}=n\overrightarrow{B}$ ; where $n$ is a constant.

Now, taking given vectors we have

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

$\overrightarrow{A}=-\frac{1}{2}\overrightarrow{B}$

Hence, we have value of $n=-\frac{1}{2}$. So the given vectors are colinear.