# Thread: What's the parametric equation for the line through point ...

1. ## What's the parametric equation for the line through point ...

Find the parametric equations for the line through the point p(1,4,8) that is parallel to the plane x+y+z = 8 and perpendicular to the line x = 5+t, y = 1 - t, z = 5t?

Choices
1) x = 1 + t. y = a + t, z = 8 - 2t
2) x = 1 + 6t, y = 4 + 4t, z = 8 + t
3) x = 1 - 6t, y = 4 + 4t, z = 8 + 2t
4) x = 1 + 6t, y = 4 + 4t. z = 8 + 2t
5) x = 1 - 6t, y = 4 + 4t, z = 8 + t

I thought it was #4, but I'm not sure. I got (6, 4, -6) then I did it.
Thanks

2. Well, how do you propose to solve it? What steps did you take?

3. Notice that you are given two vectors that this line must be perpendicular to.

4. x + y + z = 8 is <1,1,1> which is the natural = n
then
x = 5+t, y = 1 - t, z = 5t = <5, -1, 5> = L1
so then you do the cross product of n and L1
which I got
<6,0,-6)
At this point I am confused. I've already tried answered 2 and 4 which were both wrong. I believe I may be doing something very wrong or be confused as to what to do afterward. Thanks