- #1

Addez123

- 199

- 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.

$$z = f_x'(1, -1)(x -1) + f_y'(1, -1)(y+1) = 2(x-1) + 3(y+1)$$

Eitherway it's b that's my issue.

I can find the gradient of both plane and surface, but trying to do "dot-product 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 dot-product 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?

$$z = f_x'(1, -1)(x -1) + f_y'(1, -1)(y+1) = 2(x-1) + 3(y+1)$$

Eitherway it's b that's my issue.

I can find the gradient of both plane and surface, but trying to do "dot-product 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 dot-product 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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