Question

Write two different vectors having 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 directions cosines of $\overrightarrow{p}$ are given by,
$l=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt{3}},m=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt{3}}$, and $n=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt{3}}$.
The direction cosines of $\overrightarrow{q}$ are given by
$l=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}},m=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}}$, and $n=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}}$.
The direction cosines of $\overrightarrow{p}$ and $\overrightarrow{q}$ are the same. Hence, the two vectors have the same direction.