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`.