Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j - 12tk at a distance 52? units along the curve from the point (0,5,0) in the direction of increasing arc length. The point is (, , ). (Type exact answers, using ? as needed.)
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Given \( \mathbf{r}(t) = 5\sin(t)\mathbf{i} + 5\cos(t)\mathbf{j} + 12t\mathbf{k} \), we have \( \mathbf{r}'(t) = 5\cos(t)\mathbf{i} - 5\sin(t)\mathbf{j} + 12\mathbf{k} \). The magnitude of \( \mathbf{r}'(t) \) is \( |\mathbf{r}'(t)| = \sqrt{5^2 + (-5)^2 + 12^2} = Show more…
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