Question

Find 'm' if $\overrightarrow{P}=\hat{i}-3\hat{j}+4\hat{k}$ and $\overrightarrow{Q}=m\hat{i}-6\hat{j}+8\hat{k}$ have the same direction.

Answer 1

As the vectors have same direction ,checking for the ratios of the given corresponding components we get

For components of $\hat{k}=\frac{8}{4}$=2

For components of $\hat{j}=\frac{-6}{-3}$=2

Now equating the unknown component with the common ratio we get

For components of $\hat{i}=\frac{m}{1}$=2

Thus the unknown component m=2