I have to find an equation for a plane normal to the vector $\vec{r(t)} = \langle e^{t}sin(\frac{\pi t}{2}),e^{t}cos(\frac{\pi t}{2}),t^{2}\rangle$ when $t=1$. I know I have to find the derivative and then plug in the value for t such that $\vec{r'(1)}$, then use each coordinate of the point with this vector to determine an equation. But since I don't have a point I don't know how to proceed. What is the best way to tackle this?
2026-05-13 17:31:21.1778693481
Find an equation of a plane normal to a given vector
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The equation is $r'(1) \centerdot ((x,y,z) - r(1)) = 0 $