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**skeske1234** Find the intersection of pi1, pi2, pi3, and describe geometrically in each case.

a) pi1: x-y+2z=7

pi2: 2x+y-z=3

pi3: x+y+z=9

b) pi1: x+y-z=3

pi2: 2x-y+z=5

pi3: x-2y+2z=6

so this is my work:

a)

n1: (1,-1,2)

n2: (2,1,-1)

n3: (1,1,1)

b)

n1: (1,1,-1)

n2: (2,-1,1)

n3: (1,-2,2)

ok, now I can't find any way that both a) and b) have intersections because n1, n2, n3 are never parallel or have n1=kn2=kn3 .. i think i'm doing something wrong here. please help me out and demonstrate the correct method to this question. thanks in advance!