The position vectors of A, B, C and D are `2hati +3hatj +5hatk, hati + 2hatj + 3hatk, -5hati +4hatj-2hatk, hati+10hatj+10hatk`. Show that AB is parallel to CD.

The position vectors of the points A, B, C and D are 4hati+3hatj-hatk , 5hati+2hatj+2hatk , 2hati-2hatj-3hatk and 4hati-4hatj+3hatk respectively. Show that AB and CD are parallel.

If the position vectors of A, B, C, D are 3hat i +2 hat j+hatk, 4 hati +5hatj+5hatk, 4hati +2hatj -2hatk, 6hati +5hatj-hatk respec-tively then the position vector of the point of intersection of lines AB and CD is

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 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 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 and D are hati+3hatj-hatk, -hati-hatj+hatk, 2hati-3hatj+3hatk and -3hati+2hatj+hatk respectively. Then, the ratio of the moduli of the vectors vec(AB) and vec(CD) is -

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

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

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

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