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**icelated** I have to find an equation for a plane normal to$\displaystyle r(t)=< e^t sin(\frac{\pi{}}2{t}), e^t cos(\frac{\pi{}}2{t}), t^2 > $

when $\displaystyle t=1$

Is the equation in the form:

$\displaystyle <a,b,c> . <x,y,z> - r(1) = 0?$

would i take the derivative of x, y, and z?

Would this require the product rule for x, and y individually? not z of course!

here is my attempt at just the product rule of x alone:

$\displaystyle e^t d/dx(sin(\frac{\pi{}}2{t}) + sin(\frac{\pi{}}2{t}) . d/dx (e^t) $

would it then be?

$\displaystyle e^t cos(\frac{\pi{}}2{t}) + e^t sin(\frac{\pi{}}2{t}) $