Question

Write two different vectors having the same direction.

Answer 1

Consider $\overrightarrow p=(\hat i+\hat j+\hat k)$ and $\overrightarrow q=(2\hat i+2\hat j+2\hat k)$.

The direction cosines of $\overrightarrow p$ are given by,

$I=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt 3}$, $m=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt 3}$, and $n=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt 3}$.

The direction cosines of $\overrightarrow q$ are given by

$I=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt3}\frac{1}{\sqrt 3}$, $m=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt3}\frac{1}{\sqrt 3}$, and $n=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt3}\frac{1}{\sqrt 3}$.

The direction cosines of $\overrightarrow p$ and $\overrightarrow q$ are the same. Hence, the two vectors have the same direction.