Find the intersection of the two planes with equations 5(x − 1) + 2y + (z + 1) = 0 and (x − 1) + 7y − (z + 1) = 0. (use the parameter t. enter your answers as a comma-separated list of equations.)

Given:
P1: 5(x-1)+2y+1(z+1)=0
P2: 1(x-1)+7y-1(z+1)=0
Need the intersection of the planes P1 and P2 (a line)

By inspection of the equations, 
normal to P1: N1<5,2,1>
normal to P2: N2<1,7,-1>
Direction vector, V, of the required line is the cross product of P1 & P2:
   i  j   k
  5 2  1
  1 7 -1
=V<-9, 6, 33>

Since P1 passes through point (1,0,-1), the parametric equation of the required line is <1-9t, 0+6t, -1+33t>

L: 

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