# How come the normal vector of the normal plane is the derivative of the curve r(t)?

doesn't the normal plane defines all the tangents or directional derivatives at the point t of a 3 dimensional curve?

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@Math: Well, that's what my second paragraph says. $r'(t)$ is tangent to the curve. If we want our plane to be normal to the curve, it should be normal to a vector that is tangent to the curve. Try to picture it in your head or maybe make a drawing. That usually helps. –  Javier Nov 28 '12 at 3:08