Planar Intersections-Please help

May 2010
36
0
Find the equation of the plane that passes through the line of intersection of the planes x - 3y - 2z - 1 = 0 and 2x + 4y + z - 5 = 0 and parallel to the x-axis.


Find the line of intersection for the two planes:
1: 0t 3 − 2 − 1 = 0
2: 2 + 4 + − 5 = 0
let = (a scalar)
0+3 − 2 − 1 = 0…(1)
2 + 4 + − 5 = 0.….(2)
use substitution to find the value of y from equation (1):
0+3 − 2 − 1 = 0…………..(1)
3= 2+ 1
=2+13………(3)
eliminate the variable y from the equations:
First Multiply equation (1) by 4, and multiply equation (2) by -3:
0+12 −8 − 4 = 0
−6−12−3+15 = 0
Use the elimination method:
0+12 −8 − 4 = 0
−6−12−3+15 = 0
−6−11+11=0
−6−11=−11…(4)
−11=−11+6
=−6/11+1
y:
Substitute the value of z into equation (3):
=2+13
=2(−6/11+1)
=(−4−11)/11

I am very confused by the decimal values...Does my working make sense? I would appreciate any help
 
Nov 2009
202
20
Find the equation of the plane that passes through the line of intersection of the planes x - 3y - 2z - 1 = 0 and 2x + 4y + z - 5 = 0 and parallel to the x-axis.


Find the line of intersection for the two planes:
1: 0t 3 − 2 − 1 = 0
2: 2 + 4 + − 5 = 0
let = (a scalar)
0+3 − 2 − 1 = 0…(1)
2 + 4 + − 5 = 0.….(2)
use substitution to find the value of y from equation (1):
0+3 − 2 − 1 = 0…………..(1)
3= 2+ 1
=2+13………(3)
eliminate the variable y from the equations:
First Multiply equation (1) by 4, and multiply equation (2) by -3:
0+12 −8 − 4 = 0
−6−12−3+15 = 0
Use the elimination method:
0+12 −8 − 4 = 0
−6−12−3+15 = 0
−6−11+11=0
−6−11=−11…(4)
−11=−11+6
=−6/11+1
y:
Substitute the value of z into equation (3):
=2+13
=2(−6/11+1)
=(−4−11)/11

I am very confused by the decimal values...Does my working make sense? I would appreciate any help
Any equation of a plane passing through the intersection of 2 planes is given by (x-3y-2z-1)+(lambda)(2x+4y+z-5)=0 where lambda=l be any constant.Simplifying we get x(1+2l)+y(4l-3)+z(l-2)-6l=0-------(1).But it is given that the resulting plane is parallel to the x-axis. therefore the coefficient of y in (1) must be 0. thus 4l-3=0 =>l=3/4. Putting this value in (1) we should the value of the required plane which according to my calculations is:10x-5z-18=0. Hope this was helpful!!!