Find the parametric equations of the line that passes throug

Solution

Since we have the plane 5x+2y+3z=1 , we know that the vector [5, 2, 3] is perpendicular to the plane so we get parametric eq with the point (2,1,3) as x = 2+5t, y = 1+ 2t, z = 3+3t solving for t, we get eq of line (x-1)/5 = (y-1)/2 = (z-3)/3