Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

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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  • 9 years ago
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    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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