 #1
Addez123
 198
 21
 Homework Statement:

Given function surface:
$$z = x^2 + y^2$$
a. Find tangent plane in point (1, 1)
b. Find all points where the tangentplane of the surface is parallel to the plane:
$$2x + 3y  z = 135$$
 Relevant Equations:
 Math and stuff.
a. I solved a but I don't fully understand how it works.
$$z = f_x'(1, 1)(x 1) + f_y'(1, 1)(y+1) = 2(x1) + 3(y+1)$$
Eitherway it's b that's my issue.
I can find the gradient of both plane and surface, but trying to do "dotproduct of both normals = 1" will give an equation involving two complex square roots and I rather just not. Because I remember there was an easier way!
I don't completely remember what it was, but my solution would be find two vectors within the surface and the dotproduct of each of them with the plane normal must equal 0. But how would I find two vectors in the surface without doing excrusiating many equations? I suppose it has something to do with the answer in a, but I just can't think of anything!
Basically, I know this can be solved in a single equation given by normal vector and the function surface (or its gradient), I just don't remember which. Can someone give me a hand?
$$z = f_x'(1, 1)(x 1) + f_y'(1, 1)(y+1) = 2(x1) + 3(y+1)$$
Eitherway it's b that's my issue.
I can find the gradient of both plane and surface, but trying to do "dotproduct of both normals = 1" will give an equation involving two complex square roots and I rather just not. Because I remember there was an easier way!
I don't completely remember what it was, but my solution would be find two vectors within the surface and the dotproduct of each of them with the plane normal must equal 0. But how would I find two vectors in the surface without doing excrusiating many equations? I suppose it has something to do with the answer in a, but I just can't think of anything!
Basically, I know this can be solved in a single equation given by normal vector and the function surface (or its gradient), I just don't remember which. Can someone give me a hand?
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