# parallel lines to planes

• September 8th 2009, 09:16 PM
arizona11
parallel lines to planes
How do I figure out if a line is parallel to a plane?
An example equation could be:

line: x=(4, 3, 8) + t(4, 6, -18)
plane: x= (9, 3, 7) + k(6, 5, 9) + t(8, 8, 3)

Thanks for the help!
• September 8th 2009, 10:13 PM
CaptainBlack
Quote:

Originally Posted by arizona11
How do I figure out if a line is parallel to a plane?
An example equation could be:

line: x=(4, 3, 8) + t(4, 6, -18)
plane: x= (9, 3, 7) + k(6, 5, 9) + t(8, 8, 3)

Thanks for the help!

1. Show that the system of linear equations:

$(4, 3, 8) + t(4, 6, -18)= (9, 3, 7) + u(6, 5, 9) + v(8, 8, 3)$

has no solutions.

2. Show that the mininmum distance between the line and plane $>0$

CB