Proving coplanarity of four points

Coplanarity of points

Position vectors of four points A,B,C,D are 4hati +5hatj+hatk,-(hatj+hatk),3hati+9hatj+4hatk and 4(-hati+hatj+hatk) respectively . Prove that they are coplanar.

Coplanar points are the points that are in the same plane.Thus,Can 150 points be coplanar? Can 3 points be non-coplanar?

Coplanar points are the points that are in the same plane. Thus, Can 150 points be coplanar? Can 3 points be non-coplanar?

bara,barb,barc are non coplanar vectors. Prove that the four points -bara+4barb-3barc , 3bara+2barb-5barc , -3bara+8barb-5barc , -3bara+2barb+barc are co-planar.

Prove that the four points (4hati + 5 hatj+hatk), - (hatj +hatk),(3hati+9hatj+4hatk) and 4 (-hati+hatj+hatk) are coplanar.

Prove that the four points 4bari + 5barj +bark, - (barj + bark) , 3bari + 9barj + 4bark , - 4bari + 4barj +4bark are coplanar.

Prove that the four points 4veci+5veci+veck, -(vecj+veck),3veci+9vecj+4veck and 4(-veci+vecj+veck) are coplanar

Prove that the four points 4veci+5veci+veck, -(vecj+veck),3veci+9vecj+4veck and 4(-veci+vecj+veck) are coplanar

Prove that the four points with position vectors 2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc and veca-6vecb+6vecc are coplanar.