If a vector $\vec{v} = 3\hat{i} + 4\hat{j} - 5\hat{k}$ is rotated about the origin, its magnitude remains constant. If the new vector is $\vec{v}' = (a + 1)\hat{i} - 3\hat{j} + 5\hat{k}$, find the possible values of $a$.
- A$5 \text{ or } 3$
- B$5 \text{ or } -3$
- C$4 \text{ or } -2$
- D$-5 \text{ or } 3$
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