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 a line passing through the point (1,2,3) and perpendicular to the plane vecr.(2hati-3hatj+4hatk) = 1 .

Find the equation of a line passing through the point (1,2,3) and perpendicular to the plane vecr.(2hati-3hatj+4hatk) = 1 .

Prove that the plane vecr*(hati+2hatj-hatk)=3 contains the line vecr=hati+hatj+lamda(2hati+hatj+4hatk).

Prove that the plane vecr*(hati+2hatj-hatk)=3 contains the line vecr=hati+hatj+lamda(2hati+hatj+4hatk).

Prove that the plane vecr*(hati+2hatj-hatk)=3 contains the line vecr=hati+hatj+lamda(2hati+hatj+4hatk).

Find the equation of the plane passing through the point (1,1,1) and containing the line: vecr=(-3hati+hatj+5hatk)+lambda (3hati-hatj+5hatk) . Also, show that the plane contains the line: vecr=(-hati+2hatj+5hatk)+lambda(hati-2hatj-5hatk) .

Find the equation of the plane passing through the point (3, 4, -1) and parallel to the plane vecr.(2hati-3hatj+5hatk)+2=0

Find the equation of plane passing through the point (-1,-1,2) and perpendicular to each of the plane vecr(2hatj-3hatk)=2 and vecr.(5hati-4hatj+hatk)=6

Find the equation of the plane passing through the point hati-hatj+hatk and perpendicular to the vectro 3hati-hatj-2hatk and show that the point 2hati+4hatj lies on the plane.

Find the equation of the plane passing through the point hati-hatj+hatk and perpendicular to the vectro 3hati-hatj-2hatk and show that the point 2hati+4hatj lies on the plane.