The position vectors of the point P,Q,R and S are respectively `hati+hatj+hatk, 2hati+5hatj, 3hati+2hatj-3hatk and hati-6hatj-hatk`. Prove that the lines PQ and RS are parallel and the ratio of their length is `1/2`

The position vectors of the points P,Q,R,S are hati+hatj+hatk, 2hati+5hatj,3hati+2hatj-3hatk and hati-6hatj-hatk. Prove that the lines PQ and RS are prallel and find the ratio of their lengths.

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, 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, C are 2 hati + hatj - hatk , 3 hati - 2 hatj + hatk and hati + 4hatj - 3 hatk respectively . These 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.

If position vectors of P,Q,R,S be respectively 2hati+4hatk, 5hati+4hatj+4hatk, -4hati-8hatj+hatk, 2hati+hatk , prove that RS is parallel to PQ and is twice of PQ.

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 .

If the figure formed by the four points hati+hatj-hatk,2hati+3hatj,3hati+5hatj-2hatk and hatk-hatj is

Prove that: (2hati+3hatj)xx(hati+2hatj)=hatk

Prove that points hati+2hatj-3hatk, 2hati-hatj+hatk and 2hati+5hatj-hatk form a triangle in space.