Posted by **Mackenzie** on Tuesday, December 4, 2012 at 5:40pm.

Find the parametric equations for the line of intersection of the planes x+y+z=3 and x-y+2z=2

I took the cross product of the 2 equations and got 3i-j-2k

I then set z=0 and got x=5/2 and y=1/2.

I got:

x=5/2 +3t

y=1/2-t

z=-2t

However, the answers are supposed to be:

x=5/2-(3/2)t

y=1/2+(1/2)t

z=t

What is my procedure missing to get there?

- Calculus -
**A.**, Tuesday, December 4, 2012 at 6:09pm
I think your method is correct.

You took the cross product of the two vectors of the plane <1,1,1>x<1,-1,2> and got the direction vector v=<3,-1,-2>

You combined the two equations and got (0,5/2,1/2), which gives you the position

There are many different solutions for an equation of a line. So dont think that your answer is wrong.

- Calculus -
**A.**, Tuesday, December 4, 2012 at 6:12pm
*oops (5/2,1/2,0) for position

Looking at the answer again,

it looks like they divided the vector by 2

- Calculus -
**Mackenzie**, Tuesday, December 4, 2012 at 6:22pm
Do you know why they divided it by 2?

## Answer this Question

## Related Questions

- Calculus - Find the parametric equations for the line of intersection of the ...
- Calculus - Consider the planes given by the equations 2y−2x−z=2 x&#...
- Math - Find parametric equations and symmetric equations for the line of ...
- vectors - 3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the ...
- Vectors - 3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the ...
- Math - Intersection of planes - Find the vector equation of the line of ...
- maths - geometry - In a space with an orthonormal coordinate system consider the...
- Math - intersection of planes - You are given the following two planes: x+4y-3z-...
- Calculus - 1. a) Write the vector and parametric equations of the line through ...
- math - a vector parallel to the line of intersection of the planes. x-2y-z=6 and...