# Find an equation of a plane normal to a given vector

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?

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You need to find the plane passing through $r(1)$ that is perpendicular to the vector $r'(1)$. I am guessing that you meant $r$, not $r'$ above? –  copper.hat May 25 '12 at 6:50
oops. yes. sorry about that. –  Dylan May 25 '12 at 7:01
I am still not clear on how to find this since you simply restated the question. All of the examples in the book give a known point to start with. Thanks. –  Dylan May 25 '12 at 7:04
I'm not sure what point you are looking for. The point $r(1) = (e,0,1)$ is on the plane. –  copper.hat May 25 '12 at 7:10

## 1 Answer

The equation is $r'(1) \centerdot ((x,y,z) - r(1)) = 0$

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I see. r(1) itself is the point. That makes sense now. –  Dylan May 25 '12 at 7:12