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The formula for a tangent plane to a surface

  1. Aug 24, 2009 #1
    Hey I'm trying to understand how we arrive at the formula for the tangent plane to a surface. An image of what i'm talking about it shown below.

    I think understand all the parts up to part c, but i don't see how we arrive at that final formula. The image of first part of the solution is shown just to provide context.

    Screenshot (14h 10m 36s).jpg

    Screenshot (14h 07m 23s).jpg
     
  2. jcsd
  3. Aug 30, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hey Mazzur! Welcome to PF! :smile:

    ∂f/dx|ro ∂f/dy|ro and ∂f/dz|ro are all constants, and they are the constants that have to be the coefficients of x y and z …

    that's the bit you understand, isn't it? :wink:

    So the equation has to be
    ∂f/dx|rox + ∂f/dy|ro y + ∂f/dz|roz = constant,

    and all they've done is to put that constant on the left of the = sign, and split it up between the three coordinates.

    If you prefer, you can put it back on the right, like this …

    ∂f/dx|rox + ∂f/dy|ro y + ∂f/dz|roz = ∂f/dx|roxo + ∂f/dy|ro yo + ∂f/dz|rozo

    either way, you can see that putting x = xo, y = yo, z = zo, makes the equation true. :smile:
     
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