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.

Question

asked Feb 27, 2021 167k views

1 Answer

Siva Kandaraj · Answer 1 · 2021-03-05T04:52:26+0000

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
and
.