## Find Find the point in this plane where it intersects the z axis

1. The problem statement, all variables and given/known data

find the point in this plane where it intersects the z axis (x=y=0).

P = {<x;y;z;> = <1;-1;0;> + a<1;-2;0;> + b<2;0;-1;> , for all a,b}

(by <l;m;n;> i mean to denote a column)

2. Relevant equations

3. The attempt at a solution
I talked to my TA last friday and he made it seem easy, but I don't remember what he said anymore. I have something that looks like

I set up a matrix that looks like

[<1;-1;0;> <1;-2;0;> <2;0;-1;>] [<1;a;b>] = [<0;0;2;>]

I'm not really sure what to do from here. It says it is asking for a point, does this mean which (a,b) works? What can you help me with?

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 Recognitions: Homework Help find (a,b) where it works by row-reducing your matrix then use (a,b) in P= P(a,b)== a & b are parameters in the parameterisation of the plane, each (a,b) corresponds to a point on the plane P

Mentor
 Quote by montana111 1. The problem statement, all variables and given/known data find the point in this plane where it intersects the z axis (x=y=0). P = { = <1;-1;0;> + a<1;-2;0;> + b<2;0;-1;> , for all a,b} (by i mean to denote a column) ...
This is all you should need.
<x;y;z;> = <1;-1;0;> + a<1;-2;0;> + b<2;0;-1;>
It says that
x = 1 + 1∙a + 2∙b

y = -1 - 2∙a + 0∙b

z = 0 + 0∙a - 1∙b
Now "Find the point in this plane where it intersects the z axis (x=y=0)." So, find what a & b make this happen?

Edited per ehild's note.

Thanks goes to ehild.

Recognitions:
Homework Help

## Find Find the point in this plane where it intersects the z axis

 Quote by SammyS This is all you should need. = <1;-1;0;> + a<1;-2;0;> + b<2;0;-1;> It says thatx = 1 + 1∙a + 2∙b y = -1 - 2∙a - 2∙b z = 0 + 0∙a - 1∙b
SammyS,

There is a typo in your equations (shown in red)

It should be

y=-1-2∙a +0∙b

ehild

 Tags linear algebra, matrix, plane, z axis