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Hyperboloid problem

  • Thread starter bodensee9
  • Start date
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1. Homework Statement
Hello, can someone tell me where I went wrong? So, I am supposed to find the points on the hyperboloid x^2-y^2+2z^2 = 1 where the normal line is parallel to the line that joins the points (3,-1,0) and (5,3,6).


2. Homework Equations
I think I'm supposed to find the gradient vector of the hyperboloid, because that has the direction of the normal line.


3. The Attempt at a Solution
So, if I'm right, the gradient of the hyperboloid is <2x, -2y, 2z>, and that is supposed to have the same direction as the vector <2, 4, 6>. So, wouldn't I just be looking for values of x, y, and z that is in multiples of <2, 4, 6>? That seems wrong to me. Thanks!!!
 

Answers and Replies

AKG
Science Advisor
Homework Helper
2,559
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Wouldn't the gradient be <2x, -2y, 4z>? Then you'd need to find (x,y,z) such that <2x, -2y, 4z> is a scalar multiple of <2, 4, 6> AND (x,y,z) must lie on the given hyperboloid, i.e. it must satisfy x2 - y2 + 2z2 = 1.
 

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