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# Mathematics! Calculus?

Find the equation of the tangent plane and the equation of the normal line at the

point P0(1, 0, 1) on the surface (x, y, z) such that 3z+x^2=4

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- No MythologyLv 79 years agoFavorite Answer
Calling the left side of the equation of the surface f(x, y, z)

∇f = 2x i + 3 k.

At (1, 0, 1), this gives the normal vector <2, 0, 3>. The normal line is given parametrically by

x = 1 + 2t, y = 0, z = 1 + 3t, -∞ < t < ∞.

You can express that as a vector valued function if you wish.

The tangent plane has equation

2(x - 1) + 0(y - 0) + 3(z - 1) = 0 ==> 2x + 3z = 5.

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