(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the equations of the normal lines to the surfaces at the given points.

z=(3/4)x^2+3y^2 @ pt. (2,1)

2. The attempt at a solution

I have already found the equation of the tangent plane and know it is correct.

Tangent plane => (z-6)=3(x-2)+6(y-1)

Now, I am confused here, when it says it wants the equation of the line normal to the surface, it really wants the equation of the line normal to the tangent plane correct?

I know that the answer is <3t+2, 6t+1, -t+6> but I have no idea how to solve for it.

I understand where these values come from <3t+2,6t+1,-1t+6> but what step am I missing to switch the signs of the x[tex]_{}0[/tex] y[tex]_{}0[/tex] and z[tex]_{}0[/tex]

I need to be able to do this again on 7 more problems, 4 of which are from parameterizations (i dont think this maters). For those, I took the partial derivatives of the position vector and crossed them, is the result of the cross product the equation of the line normal to the surface at that point?

I think I have a solid grasp on the actual image of what im looking for, but i dont understand how to actually get it.

Note: This HW was assigned before we learned about Gradients.

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# Homework Help: Calc 3-normal lines to surfaces

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