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.

If the position vectors of A and B respectively hati+3hatj-7hatk and 5 hati-2hatj+4hatk , then find AB

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

If vectors A and B be respectively equal to 3hati - 4hatj + 5hatk and 2hati + 3hatj - 4hatk. Find the unit vector parallel t A + B

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.

If the position vectors of the vertices of a triangle be 2hati+4hatj-hatk,4hati+5hatj+hatk and 3 hati+6hatj-3hatk , then the triangle is

If the position vectors of P and Q are (hati+3hatj-7hatk) and (5hati-2hatj+4hatk) , then |PQ| is

The points with position vectors alpha hati+hatj+hatk, hati-hatj-hatk, hati+2hatj-hatk, hati+hatj+betahatk are coplanar if

If the vectors 2hati-hatj+hatk,hati+2hatj-3hatk and 3hati+ahatj+5hatk are coplanar, the prove that a=-4.

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 .

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