The position vector $\vec{p}$ of a point $(24, n)$ in a 2D plane is given by: $$ \vec{p} = 24\hat{i} + n\hat{j} $$
The magnitude of a vector $\vec{p} = x\hat{i} + y\hat{j}$ is given by $|\vec{p}| = \sqrt{x^2 + y^2}$. Given $|\vec{p}| = 25$, we have: $$ \sqrt{24^2 + n^2} = 25 $$
Squaring both sides: $$ 24^2 + n^2 = 25^2 $$ $$ 576 + n^2 = 625 $$ $$ n^2 = 625 - 576 $$ $$ n^2 = 49 $$ $$ n = \pm \sqrt{49} = \pm 7 $$
Final Answer: \pm 7
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