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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!!!