Question

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

• A. True
• B. False

Answer 1

The correct option is A True

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

We observe, $\overrightarrow{b}=-4\hat{i}+6\hat{j}-8\hat{k}=2(2\hat{i}-3\hat{j}+4\hat{k})=-2\overrightarrow{a}$

Therefore, $\overrightarrow{b}=\lambda \overrightarrow{a}$ where $\lambda =-2$

Hence, the given vectors are collinear.