Write two different vectors having the same magnitude.

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 the magnitude of $\vec{a}$ is $|\vec{a}| = \sqrt{1^{2} + 2^{2} + 3^{2}} = \sqrt{1 + 4 + 9} = \sqrt{14}$.
The magnitude of $\vec{b}$ is $|\vec{b}| = \sqrt{2^{2} + (-1)^{2} + (-3)^{2}} = \sqrt{4 + 1 + 9} = \sqrt{14}$.
Since $|\vec{a}| = |\vec{b}| = \sqrt{14}$ and the components are different,$\vec{a}$ and $\vec{b}$ are two different vectors having the same magnitude.