Posted by **Shaila** on Monday, September 6, 2010 at 1:11pm.

You are given the following two planes:

x+4y-3z-12=0

x+6y-2z-22=0

a) Determine if the planes are parallel

b) Fine the line of intersection of the two

- Math - intersection of planes -
**MathMate**, Monday, September 6, 2010 at 1:26pm
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=5t-8

y=-(1/2)t+5

z=t

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