Write two different vectors having same magnitude.
Question:

Write two different vectors having same magnitude.

Solution:

Consider $\vec{a}=(\hat{i}-2 \hat{j}+3 \hat{k})$ and $\vec{b}=(2 \hat{i}+\hat{j}-3 \hat{k})$.

It can be observed that $|\vec{a}|=\sqrt{1^{2}+(-2)^{2}+3^{2}}=\sqrt{1+4+9}=\sqrt{14}$ and

$|\vec{b}|=\sqrt{2^{2}+1^{2}+(-3)^{2}}=\sqrt{4+1+9}=\sqrt{14}$

Hence, $\vec{a}$ and $\vec{b}$ are two different vectors having the same magnitude. The vectors are different because they have different directions.