Question

Find the equation of the plane that passes through the point (2,1,3) and contains the line x=1+t, y=2+2t, z=-1+3t. Write your answer in the form ax+by+cz+d=0 with the simplified numbers and a > 0.

Answer 1

putting values of a,b and c in a(x-1) +b(y-2) + c(z +1) = 0 and dividing by    we have

-11(x-1)+1(y-2)+3(z+1) = 0 ;

-11x + y + 3z +12 = 0;

11x - y - 3z -12 = 0    is the final equation of the plane.