- #1
somebodyelse5
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Homework Statement
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 don't 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 I am looking for, but i don't understand how to actually get it.
Note: This HW was assigned before we learned about Gradients.