Find the points on the sphere x2 + y2 + z2 = 1 where the tangent plane is parallel to the plane 2x + y - 3z = 2.
z - z0 = fx(x0, y0)(x - x0) + fy(x0, y0)(y - y0))
That's all I believe
The Attempt at a Solution
This chapter in our text does not require the use of vectors (eg dot and cross product), so I need to do this strictly algebraically. I found both first order partials, but didn't really know what to do after that. I plug in these partials to the expression above, but I don't think it's possible to solve for x0 and y0 explicitly.
If someone could guide me in the right direction, it would be much appreciated. Thank you all in advance!