Verify that a line lies wholly in a plane

woollybull · #1 $Old$ 11-16-2008, 04:07 AM

1. Verify that the line with equation r= 2i +4j +k + t(-4i + 4j -
5k) lies wholly in the plane with equation 3x -2y +4z = 2.

I rearranged r to be r = i(-4t-1) + j(4t+4) + k(-5t+1)
I substitued this each component into 3x -2y +4z and got
3(-4t-1) - 2(4t+4) + 4(-5t+1)= -40t + 2

I was hoping to get 2 which would show that it is wholly in the
plane. Is that wrong??

Thankyou.

Plato · #2 $Old$ 11-16-2008, 05:45 AM

Quote:

Originally Posted by woollybull $View Post$

1. Verify that the line with equation r= 2i +4j +k + t(-4i + 4j - 5k) lies wholly in the plane
with equation 3x -2y +4z = 2.
I rearranged r to be r = i(-4t-1) + j(4t+4) + k(-5t+1)

There is a small mistake: x=-4t+2

woollybull · #3 $Old$ 11-16-2008, 08:36 PM

Hey thanks!! I did check it several times as well!