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Component functions and coordinates of linear transformation

  1. Feb 19, 2015 #1
    Let A(a, b, c) and A'(a′,b′,c′) be two distinct points in R3. Let f from [0 , 1] to R3 be defined by f(t) = (1 -t) A + t A'. Instead of calling the component functions of f ,(f1, f2, f3) let us simply write f = (x, y, z). Express x; y; z in terms of the coordinates of A and A, and t. I thought that a is the partial derivative of f1 with respect to x, b is the partial derivative of f2 with respect to y, and c is the partial derivative of f3 with respect to z. I am right? Any hint how to find the relation and to find the derivative of f?
     
    Last edited: Feb 19, 2015
  2. jcsd
  3. Feb 19, 2015 #2

    Dick

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    I don't see why you think partial derivatives come into this. ##(1-t)A=(1-t)(a,b,c)=((1-t)a,(1-t)b,(1-t)c)##. Now do something similar for ##tA'## and just add them.
     
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