Intersecting planes in 3-d space

[megr_ftw]

Homework Statement

Find the vector equation for the line of intersection of the planes x + 4y - 2z = 5 and
x + 3z = -5
r= (__,__,0) + t(12,__,__)

Homework Equations

equation of a plane= a(x-x₀)+b(y-y₀)+c(z-z₀)= 0

The Attempt at a Solution

Do I need to convert the equations of the planes into parametric equations?

 

[Gregg]

Find a vector that is parallel to both planes then find a common point to both planes.

 

[HallsofIvy]

Homework Statement

Find the vector equation for the line of intersection of the planes x + 4y - 2z = 5 and
x + 3z = -5
r= (__,__,0) + t(12,__,__)

Homework Equations

equation of a plane= a(x-x₀)+b(y-y₀)+c(z-z₀)= 0

The Attempt at a Solution

Do I need to convert the equations of the planes into parametric equations?

No, you don't need parametric equations for the planes but you do need parametric equations for the line of intersection. The simplest way to do this is to solve the two equations. For example, subtracting the first equation from the second eliminates x given 4y- 5z= 10 or y= (5z+ 10)/2. Because there are only two equations you cannot solve for y or z separtely but you can put y= (5z+10)/2 back into either of the first equations and solve for x as a function of z. Then use z itself as parameter!