Question: Tangent Planes T(P) will be less important in our work, but you should know how to represent them. (a) If S: r(u, v), then T(P):

Tangent Planes T(P) will be less important in our work, but you should know how to represent them.

(a) If S: r(u, v), then T(P): (r* - r   ru    rv) = 0 (a scalar triple product) or r*(p, q) = r(P) + pru(P) + qrv(P).

(b) If S: g(x, y, z) = 0, then T(P): (r* - r(P)) · ∇g = 0.

(c) If S: z = f(x, y), then T(P): z* - z = (x* - x)fx(P) + (y* - y)fy(P).

Interpret (a)-(c) geometrically. Give two examples for (a), two for (b), and two for (c).

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