Question

Find a set of parametric equations of the line with the given characteristics. (Use t for the parameter. Enter your answers as a comma-separated list of equations.) The line passes through the point (−8, 5, 2) and is perpendicular to the plane given by −x + 8y + z = 5.

Answer 1

The parametric equations of line are x=-8-t, y=5+8t and z=2+t.

Explanation:

It is given that the line passes through the point (−8, 5, 2) and is perpendicular to the plane given by −x + 8y + z = 5.

The coordinate of point are (−8, 5, 2).

Normal vector = <-1,8,1>

The position vector of a line is

`\overrightarrow{r}=(x_0,y_0,z_0)+t<a,b,c>`

then the parametric equations of line are
`x=x_0+at,y=y_0+bt,z=z_0+ct`.

Where, (x_0,y_0,z_0) are the coordinate of point and <a,b,c> is normal vector.

The position vector of given line is

`\overrightarrow{r}=(-8,5,2)+t<-1,8,1>`

The parametric equations of line are

`x=-8-t`

`y=5+8t`

`z=2+t`

Therefore the parametric equations of line are x=-8-t, y=5+8t and z=2+t.