# Linear algebra, point of intersection

1. Mar 7, 2009

### cleopatra

1. The problem statement, all variables and given/known data
1) x=3+t
y=2-4t
z=-5+11t

2)12x+10y-4z

Find the point where these two lines intersect.

2. Mar 7, 2009

### cleopatra

I mean, where the line in 1 and plan in 2 intersect

3. Mar 7, 2009

### yyat

Last edited by a moderator: Apr 24, 2017
4. Mar 7, 2009

### cleopatra

=48

but I don´t think that matters

5. Mar 7, 2009

### yyat

It does matter. The equation 12x+10y-4z=48 defines a different (but parallel) plane then the equation 12x+10y-4z=0. For example the second one passes through the origin while the first does not (to see this, just check if x=0,y=0,z=0 satisfies the equation).

6. Mar 7, 2009

### cleopatra

okey thanks

but do you know how to solve it?

7. Mar 7, 2009

### yyat

This is a system of linear equations (4 equations, 4 unknowns). I am almost sure you have solved systems of linear equations before, for example when intersecting two lines in the plane:

2x+y=1
x-3y=0

How did you do that? Hint: Substitution. Your problem can be solved in a similar way.

8. Mar 7, 2009

### cleopatra

I really haven´t solved anything like this. I´m a beginner.
I just really need a good teacher to show me how to do this.
Can you? Or if you can´t solve it, can anybody else?
And, the answer of the plane is =46, not 48.

9. Mar 7, 2009

### lanedance

you have an equation for a plane

ax + by + cz = d
a,b,c,d constants

and a line (x(t),y(t),z(t))

what happens when we are on both the plane & line? bothe equations will be solved

substitute your line components (x(t),y(t),z(t)) into the equation of the plane & solve for t

this give the point on the line in terms on twhere the plane & line intersect

10. Mar 7, 2009

### Dick

Put your expressions for x, y and z in terms of t into the equation of the plane. Then solve for t.

11. Mar 8, 2009

### cleopatra

Anyone who can show me some equations?