Component functions and coordinates of linear transformation

[raghad]

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?

 

[Dick]

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?

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.