# Simple parametrization problem

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• December 5th 2009, 11:13 AM
messianic
Simple parametrization problem
How do I parametrize a straight line segment from (2,-1,3) to (4,2,-1)?

How do I parametrize path C from (0,0,0) to (4,2,3) that consists of three line segments parallel to x, y and z-axis in that order?

How do I parametrize path C from (-1,2,-2) to (1,5,2) that consists of three line segments parallel to the z-axis, x-axis, and y-axis in that order?

These are probably simple but I really need help
• December 6th 2009, 06:33 AM
Scott H
When we move from $(2,-1,3)$ to $(4,2,-1)$, the following changes take place:

$x$ increases $2$ units
$y$ increases $3$ units
$z$ decreases $4$ units

Now let's say we want the independent variable of the parametrized line, $t$, to range from $0$ to $1$, so that as $t$ moves from $0$ to $1$, the point $(x(t),y(t),z(t))$ will move from $(2,-1,3)$ to $(4,2,-1)$. In that case, since

$(x,y,z)=(2,-1,3)$

at $t=0$, we obtain for our parametrization

$(x,y,z)=(2+2t,-1+3t,3-4t).$

Hint for the next problem: the first line of the path is given by

$(x,y,z)=(4t,0,0).$