How do I get started?Quote:

Find the points on the surface http://webwork.asu.edu/webwork2_file...9e2a58ead1.png at which the tangent plane is parallel to the plane http://webwork.asu.edu/webwork2_file...64227b3791.png.

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- Oct 17th 2009, 09:44 PMzpwnchenpoints on the surfaceQuote:

Find the points on the surface http://webwork.asu.edu/webwork2_file...9e2a58ead1.png at which the tangent plane is parallel to the plane http://webwork.asu.edu/webwork2_file...64227b3791.png.

- Oct 17th 2009, 10:41 PMredsoxfan325
Parallel planes have the same normal vector (i.e. $\displaystyle \langle 3,3,-1\rangle$). The constant term is irrelevant.

The equation for the tangent plane is

$\displaystyle F_x(x_0,y_0,z_0)(x-x_0)+F_y(x_0,y_0,z_0)(y-y_0)+F_z(x_0,y_0,z_0)(z-z_0)=0$

$\displaystyle F_x=2x$

$\displaystyle F_y=6y$

$\displaystyle F_z=8z$

So you want $\displaystyle 2x_0=3k$, $\displaystyle 6y_0=3k$, and $\displaystyle 8z_0=-k$ (because you have to take into account the normal vector can be scaled by any constant $\displaystyle k$).

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