Question

If a vector $\overrightarrow{a}$ of magnitude $50$ is collinear with vector $\overrightarrow{b}=6\hat{i}-8\hat{j}-\frac{15}{2}\hat{k}$ and makes an acute angle with positive z - axis then :

• A. $\overrightarrow{a}=4\overrightarrow{b}$
• B. $\overrightarrow{a}=-4\overrightarrow{b}$
• C. $\overrightarrow{b}=4\overrightarrow{a}$
• D. None

Answer 1

The correct option is B $\overrightarrow{a}=-4\overrightarrow{b}$

The magnitude of $\overrightarrow{b}=\sqrt{36+64+56.25}=12.5$

We need the magnitude of $\overrightarrow{a}$ to be $50$ and so the $\overrightarrow{a}$ will be $4$ times $\overrightarrow{b}.$

Now, the direction of $\overrightarrow{a}$ will be decided by its $z$ component since it has to make an acute angle with positive $z$ axis and so its $z$ component will be positive.

Hence option $B$