5. (20 points) Let S be the unit sphere on R³. The tangent plane T of S at the point(1, 1, √2) admits

the following parametrization in terms of (x, y, z)-coordinates:

T(t, s)

Provide an implicit equation on R³ with coordinates (x, y, z) that describes the tangent plane T. Note

that there are multiple answers since the implicit equation for T is unique up to multiplication by a non-zero

scalar.

+()+()+(!)

0

+t