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## Homework Statement

Find the point of intersection of the line and the plane.

Line: x=4+k

y=2-2k

z=6+3k

Plane: x=-1-s+2t

y=1-s+4t

z=2+3s+t

## Homework Equations

None.

## The Attempt at a Solution

So I'm not that well informed with how these lines and planes behave... With that being said my attempt may be off.

What really confuses me is the parametric form of the equation of the plane. I've never seen it in this form before. I'm used to dealing with the form Ax+By+Cz+D=0. So I have no idea of what I'm suppose to do with the two variables s and t...

I tried equating the equations of the line with the equations of the plane and just got stuck with no clue of what to do.

4+k = -1-s+2t ---- Equation 1

2-2k=1-s+4t ----- Eq 2

6+3k=2+3s+t ------ Eq 3

-2 + Eq 2

---------------

-8-2k=2+2s-4t

+ 2-2k=1-s+4t

---------------

-6-4k=3+s

-------------

With no idea of what I was actually doing I decided to give up here and look through my school textbook which really didn't explain much. I also couldn't find any similar questions through googizing. I hope you guys can help me understand how to solve this question.

Thanks.