Perpendicular Lines in Three Space

[dogma]

Hello,

Please bear with me...my brain is in vapor lock.

I have a line L1 given by the following parametric equations:

x = 2+3t, y = -1+5t, z = 8+2t

I need to find the equation of a line L2 passing through point B = (1,2,5) and perpendicular to L1.

For the life of my tired, worn out brain...I cannot figure out how to determine the direction numbers that would make L2 perpendicular to L1 (with direction numbers (3,5,2)).

Can someone please give my brain a kick start.

Thanks a bunch.

dogma

 

[Data]

Any vector $(x, y, z)$ such that $(3, 5, 2) \circ (x, y, z) = 0$ has direction perpendicular to that of your line.

 

[dogma]

That makes sense, but I can see a couple of soulutions to that:

(a,b,c) = (1,-1,1), (-1,1,-1),(1,-3,6),...

If I'm on the right track, how do I determine which is correct?

Thanks again.

 

[so-crates]

That makes sense, but I can see a couple of soulutions to that:

(a,b,c) = (1,-1,1), (-1,1,-1),(1,-3,6),...

If I'm on the right track, how do I determine which is correct?

Thanks again.

Any of those would work. Pick one and figure out the intercepts.

 

[dogma]

okay, my brain is starting to show some activity...thanks all

dogma