The discussion focuses on finding the vector equation for the line of intersection of the planes defined by the equations x + 4y - 2z = 5 and x + 3z = -5. It is established that parametric equations are not required for the planes themselves but are necessary for the line of intersection. The solution involves eliminating one variable by manipulating the equations, leading to the expression for y in terms of z, allowing z to serve as the parameter for the line.
PREREQUISITESStudents studying linear algebra, geometry enthusiasts, and anyone involved in solving three-dimensional vector problems.
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!megr_ftw said: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?