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

1 Answer

  • Anonymous
    9 years ago
    Favorite Answer

    The gradient of the surface is ∇f=( 2x, 0, 3 ). Evaluating at the point (1,0,1) gives ∇f=(2,0,3) as the surface normal. The tangent plane therefore has the form 2x+3z=b, and substituting the known point gives 2(1)+3(1)=b, thus:

    Tangent plane: 2x + 3z = 5

    Normal line: ( 1+2t, 0, 1+3t )

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