This is given by the sum of the squares of its components:
$$
\|\vec{r}(t)\|^2 = (5 \cos t)^2 + (3 \sin t)^2 = 25 \cos^2 t + 9 \sin^2 t
$$
Now, we can use the trigonometric identity $\cos^2 t + \sin^2 t = 1$ to rewrite the expression:
$$
\|\vec{r}(t)\|^2 = 25
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