Question

Find two different planes whose intersection is theline:x = 6 + 3ty = -8 - 3tz = -1 - tWrite equations for each plane in the form Ax + By + C = D.

Answer 1

`x+y=-2` and
`3z-y=5` are two such planes.

Explanation:

To find the two planes whose intersection is the line

`x=6+3t\\ y=-8-3t\\ z=-1-t`

You can say that t is equal to this expression

`t=(x-6)/(3) =(y+8)/(-3)=-z-1`

Next,

`(x-6)/(3) =(y+8)/(-3)\\ (y+8)/(-3)=-z-1`

Then,

`x+y=-2` and
`3z-y=5` are two such planes.

You can see in the image attached that the intersection of this planes is the line

`x=6+3t\\ y=-8-3t\\ z=-1-t`