Question

Write parametric equations of the line through the points (7,1,-5) and (3,4,-2). please use the first point as your base-point when writing the equations.

Answer 1

Given:

A line through the points (7,1,-5) and (3,4,-2).

To find:

The parametric equations of the line.

Solution:

Direction vector for the points (7,1,-5) and (3,4,-2) is

$\vec {v}=\left<x_2-x_1,y_2-y_1,z_2-z_1\right>$

$\vec {v}=\left<3-7,4-1,-2-(-5)\right>$

$\vec {v}=\left<-4,3,3\right>$

Now, the perimetric equations for initial point $(x_0,y_0,z_0)$ with direction vector $\vec{v}=\left<a,b,c\right>$, are

$x=x_0+at$

$y=y_0+bt$

$z=z_0+ct$

The initial point is (7,1,-5) and direction vector is $\vec {v}=\left<-4,3,3\right>$. So the perimetric equations are

$x=(7)+(-4)t$

$x=7-4t$

Similarly,

$y=1+3t$

$z=-5+3t$

Therefore, the required perimetric equations are $x=7-4t, y=1+3t$ and $z=-5+3t$.