Question

Write two different vectors having same magnitude

Answer 1

Consider $\overrightarrow{a}=(\hat{i}-2\hat{j}+3\hat{k})$ and $\overrightarrow{b}=(2\hat{i}+\hat{j}-3\hat{k})$.
It can be observed that $\left|\overrightarrow{a}\right|=\sqrt{1^2+(-2{)}^2+3^2}=\sqrt{1+4+9}=\sqrt{14}$
and $\left|\overrightarrow{b}\right|=\sqrt{2^2+1^2+(-3{)}^2}=\sqrt{4+1+9}=\sqrt{14}$
Hence, $\overrightarrow{a}$ and $\overrightarrow{b}$ are two different vectors having the same magnitude. The vectors are different because they have different directions.