Find the equation of the plane through the points (2, 1, 1) and (1, 3, 4) and perpendicular to the plane `x\ \ 2y+4z=10.`

Find the vector equation of the plane through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane x-y+4z=10.

Find the vector equation of the plane through the points (2,1,-1) and (-1,3,4) and perpendicular to the plane x-2y+4z=10 .

(i) Find the equation of the plane through the points (2,-3,1) and (5,2,-1) and perpendicular to the plane x -2y + 4z = 10 . (ii) Find the vector equation of the plane through the points (2,1,-1) and (-1,3,4) and perpendicular to the plane x - 2y + 4z = 10.

Find the equation of the plane through the points A(2,1,-1) and B(-1,3,4) and perpendicular to the plane x-2y+4z=10 . Also, show that the plane thus obtained contains the line vecr=(-hati+3hatj+4hatk)+lambda(3hati-2hatj-5hatk) .

Find the equation of the plane through the points (2,2,1) and (9,3,6) and perpendicular to the plane 2x+6y+6z=1

Find the equation of the plane passing through the points (2.1,-1) and (-1,3,4) and perpendicular to the plane x-2y+2=0

Find the equation of the plane passing through the points (-1,1,1) and (1,-1,1) and perpendicular to the plane x+2y+2z=5

Find the vector equation of the plane passing through the points (2,1,-1) and (-1,3,4) and perpendicular to the plane x-2y+4z=10. Also show that the plane thus obtained contains the line vec r=-hat i+3hat j+4hat k+lambda(3hat i-2hat j-5hat k)