QUESTION:

Show that the tangent planes of the unit sphere at the points (x,y,0) are parallel to the z axis.

MY WORK:

I get the tangent planes as x^2 + y^2 = 1 ...

in R3 that's the vector (cos(t), sin(t), z) right?

And the z axis is the vector (0,0,z)

so the dot product is z^2

And the product of the magnitudes is sqrt(1 + z^2)*z

cos(theta) = z/sqrt(1+z^2) ??

But I need cos(theta) to be 1 for those vectors to be parallel...

HELP PLEASE! What have I done?