Equation of the plane passing through the points (2,2,1) and (9, 3, 6), and perpendicular to the plane 2x+6y+6z- 1=0 is

Any plane through (2,2, 1) is  a(x-2)+b(y-2)+c(z- 1)=0 -------(i)It passes through (9, 3, 6) if 7a+ b + 5c=0 --------(ii)Also (i) is perpendicular to 2x + 6y + 6z - 1 = 0, we have      2a+6b+6c=0∴     a+3b+3c=0------iii∴     a−12=b−16=c20 or a3=b4=c−5         [from (ii) and (iii)] Therefore, the required plane is 3(x - 2) + 4 (y - 2) - 5 (z- 1) = 0    or   3x + 4y - 5z -9 = 0