- #1
Aneeshrege
- 8
- 0
Homework Statement
Find the parametric equation for a line of intersection of these two planes
x+2y+3z=0
4x+5y+6z=5
Homework Equations
Normal to plane 1= <1,2,3>
Normal to plane 2= <4,5,6>
The Attempt at a Solution
I know the way to do this problem is to take cross product of two normals etc etc,
but i want to know if the way i did this is correct also.
I already turned the work in so there's nothing i can do to change it but the curiosity is killing me.
First, i set the two planes equal to each other
4x+5y+6z-5=0
x+2y+3z=0
=> x+2y+3z=4x+5y+6z-5 (please correct me my thinking process is wrong,im winging it)
=> 3x+3y+3z=5
=> x+y+z=5/3 (now I am thinking this is the equation of the intersection of the two planes but this isn't the equation of a line, it looks like a plane, or is it?)
so i took a point on this set, (5/3,0,0) and two other points (0,5/3,0) and (0,0,5/3)
i did <0,0,5/3> - <0,5/3,0> = <0,-5/3,5/3> as a directional vector.
so L(t)= (5/3,0,0) + <0,-5/3,5/3>t
x=5/3
y=-5/3t
z=5/3t
IS any of this wrong?!