Prove that a point lies on a plane given the parametric equations

[GreenTristan]

Prove that point (-2, -10, 8) lies on a plane with parametric equations x=2-t; y=2-3t; z=4+t.

Please any help on how to approach this problem.

 

[MarkFL]

Hello, and welcome to FMH!

I would begin with the \(x\)-coordinate and find the value of \(t\) that satisfies:

[MATH]-2=2-t\implies t=4[/MATH]
Now, does this value of \(t\) satisfy the other two coordinates?

 

[GreenTristan]

Okay...

so I get :

t=4

x=-2 y=-10 z=8

yes it satisfies all the coordinates.

 

[HallsofIvy]

By the way- that is a line, not a plane! There is only one parameter, not two.