Equation of a plane, given two points and a perpendicular plane

Solution 1:

make the ansatz the plane has the equation $$ax+by+cz+d=0$$ then we have $$3a+4b+c+d=0$$(1) $$3a+b-6c+d=0$$ (2) and $$[a,b,c]\cdot[7,9,4]=0$$ (3) can you proceed?