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 and hati-6hatj-hatk. Prove that the lines PQ and RS are pralel and find the ratio tof their lengths.

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.

If the position vectors of P and Q be respectively hati+3hatj-7hatk and 5hati-2hatj+4hatk and vec(PQ)

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 -

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

Find the scalar triple product vectors hati+2hatj+3hatk, hati-hatj+hatk and hati+hatj+hatk .

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