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lines in a plane

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

Reply 1

Smashing

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

...

Sorry, couldn't resist. :smile:

Reply 2

doremi

Smashing

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

...

Sorry, couldn't resist. :smile:

actually you are not excused

Reply 3

generalebriety

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

a_ix + b_iy + c_iz = d_i

, for i = 1, 2, 3, and then form a matrix equation. Under what circumstances does it have no solutions? One solution? More than one?

Reply 4

doremi

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)..