You are Here: Home >< Maths

# lines in a plane watch

1. Hi,

I am trying to find a condition for three lines in a plane to intersect in one point,

I am doing matrices, determinants, etc. and the idea is to get to a set of n linear homogenous equations in n unknowns and to say that the determinant has to be zero for their to be a a solution

but i can't get the equations

the equation of a line in a plane r = (x_0,y_0,z_0) + t(a,b,c)

where (x_0,y_0,z_0) is any point on the line and (a,b,c) is the direction vector.

I could also write the three eq's parametrically... but what good is that?

pls help
2. I've had enough of these mother****ing lines, on this mother****ing plane.

...

Sorry, couldn't resist.
3. (Original post by Smashing)
I've had enough of these mother****ing lines, on this mother****ing plane.

...

Sorry, couldn't resist.
actually you are not excused
4. I don't think you're trying to work with lines on a plane, I think you're trying to work with lines in R^3.

Assuming what you're doing is right: write each line as , for i = 1, 2, 3, and then form a matrix equation. Under what circumstances does it have no solutions? One solution? More than one?
5. Hi general..
thanks,

but your equation is that of a plane, and, as it happens, this is the previous exercise which I solved as you indicated. This one states

"Find a condition for three lines in a plane to intersect in one point" and has the hint to look at the solution to the previous exercise (the one about the planes)..

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 10, 2009
Today on TSR

### Cambridge interviews

Find out which colleges are sending invitations

### University open days

Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
• Heriot-Watt University
Wed, 21 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams