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Math Help - Intercept Proof Tangent plane

  1. #1
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    Intercept Proof Tangent plane

    I've finished this problem and I got the tangent plane equation to be

    Fx Fy Fz
    Tangent plane(at Xo,Yo,Zo) = yo*zo(x-xo) + xo*zo(y-yo) + xo*yo(z-zo)

    Not sure what the problem is asking in terms of the intercept, is it because if you multiply in Fx, Fy, Fz you get xo*yo*zo which would be the intercept?

    Thanks!
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  2. #2
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    Re: Intercept Proof Tangent plane

    Quote Originally Posted by topsaa View Post
    I've finished this problem and I got the tangent plane equation to be

    Fx Fy Fz
    Tangent plane(at Xo,Yo,Zo) = yo*zo(x-xo) + xo*zo(y-yo) + xo*yo(z-zo)

    Not sure what the problem is asking in terms of the intercept, is it because if you multiply in Fx, Fy, Fz you get xo*yo*zo which would be the intercept?

    Your plane should be written as: y_0z_0(x-x_0)+x_0z_0(y-y_0)+x_0y_0(z-z_0)=0

    Now the x\text{-intercept} of that plane is (x_1,0,0) or
    y_0z_0(x_1-x_0)-x_0z_0y_0-x_0y_0z_0=0

    From the given we know that x_0y_0z_0=1

    I admit I don't know exactly how to read the question beyond this point.
    Thanks from topsaa
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