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?