Math  intersection of planes
posted by Shaila .
You are given the following two planes:
x+4y3z12=0
x+6y2z22=0
a) Determine if the planes are parallel
b) Fine the line of intersection of the two

a. If the planes are parallel, one equation would be a linear combination of the other, which is not the case.
b. as in the previous problem,
http://www.jiskha.com/display.cgi?id=1283324887
reduce the equations to the reduced echelon form, namely
1 0 5 = 8
0 2 1 = 10
Set z=t (free variable) and solve for x, y and z to get
x=5t8
y=(1/2)t+5
z=t
Respond to this Question
Similar Questions

Calc.
Determine the interaction of the line of intersection of the planes x + y  z = 1 and 3x + y + z = 3 with the line of intersection of the planes 2x  y + 2z = 4 and 2x + 2y + z = 1. 
Calculus
Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. … 
Math  Intersection of planes
Find the vector equation of the line of intersection for the pair of planes. Plane one: x+5y3z8=0 Plane two: y+2z4=0 I did half of the work but now i am stuck. the normal of the planes are not parallel and therefore a solution exists, … 
Math  intersection of planes
You are given the following two planes: x+4y3z12=0 x+6y2z22=0 a) Determine if the planes are parallel b) Fine the line of intersection of the two planes. c) Use the two original equations to determine two other equations that have … 
Math
Determine whether the following statements are always,sometime, or never true.Explain 1.Three points determine a plane. 2.The intersection of two planes can be a point. 1.Never true, the three points must be noncollinear. 2.Never true, … 
Linear Algebra 2
This is another question I can't figure out. Given planes pie1 and pie2 defined as: pie1: 2x + 5y  7x + 2 = 0 pie2: x + y  z + 3 = 0 (b) Give the equation of the line of intersection of these two planes. I only found the answer for … 
Calculus
Consider the planes given by the equations 2y−2x−z=2 x−2y+3z=7 (a) Find a vector v parallel to the line of intersection of the planes. (b)Find the equation of a plane through the origin which is perpendicular to the … 
Vectors
which is not a possible type of intersection between three planes? 
Vectors
What is the nature of intersection of these three planes: 5x+3yz=11 2x7y+10z=2 6x+21y30z=6 I know that the answer is two parallel planes and the other one intersecting in a line. my question is how would you know that the first … 
Calculus
Consider the following planes. 5x − 4y + z = 1, 4x + y − 5z = 5 a) Find parametric equations for the line of intersection of the planes. b) Find the angle between the planes