If the position vectors of the three points A,B,C are `2hati+4hatj-hatk, hati+2hatj-3hatk and 3hati+hatj+2hatk` respectively, find a vector perpendicular to the plane ABC.

The position vectors of the points A, B, C are 2 hati + hatj - hatk , 3 hati - 2 hatj + hatk and hati + 4hatj - 3 hatk respectively . These points

The position vectors of the points A, B, and C are hati + hatj + hatk.hati+ 5hatj-hatk and 2hati + 3hatj + 5hatk , respectively . The greatest angle of triangle ABC is -

The position vectors of the points A,B, and C are hati+2hatj-hatk, hati+hatj+hatk , and 2hati+3hatj+2hatk respectively. If A is chosen as the origin, then the position vectors B and C are

The position vectors of the points A,B and C are (2hati + hatj - hatk), (3hati - 2hatj + hatk) and (hati + 4hatj - 3hatk) respectively. Show that the points A,B and C are collinear.

The position vectors of the points A,B and C are hati+2hatj-hatk,hati+hatj+hatk and 2hati+3hatj+2hatk , respectively. If A is chosen as the origin, then the position vectors of B and C are

The position vectors of vertices of a DeltaABC are 4hati - 2 hatj , hati + 4hatj - 3hatk and -hati + 5hatj + hatk respectively , then angleABC is equal to

If the position vector of the vertices A,B and C of a DeltaABC be (hati + 2hatj + 3hatk), (2hati + 3hatj + hatk) and (3hati + hatj +2hatk) respectively, prove that DeltaABC is equilateral.

The position vectors of the point A, B, C and D are 3hati-2hatj -hatk, 2hati+3hatj-4hatk, -hati+hatj+2hatk and 4hati+5hatj +lamda hatk , respectively. If the points A, B, C and D lie on a plane, find the value of lamda .