why are you working so hard?

the plane is -5x + 2y + z = 7

thus the normal vector is <-5,2,1> we want a vector that is parallel to this with coordinates <w, 1 , 1/2>

note that <w, 1, 1/2> = k<-5, 2, 1> for some constant k

plug in x = a + 1, y = a, z = a - 1, then we haveb.

5(x-a+1)-2(y-a)+0(a-1)+7=0

I now just need to solve for a, righ?

Is this anywhere close?

Thank you very much

-5(a + 1) + 2a + (a - 1) = 7

just solve for a