IF the positioin vectors of P,Q,R,S be respectively `2hati_4hatk, 5hati+3sqrt(3)hatj+4hatk,-2sqrt(3)hatj+4hatk, -2sqrt(3)hatj+hatk, 2hati+hatk` prove that RS is parallek to PQ a is two third of PQ.

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 P and Q be respectively hati+3hatj-7hatk and 5hati-2hatj+4hatk and vec(PQ)

If the positin vector of P and Q be respectively hati+3hatj-7hatk and 5hati-2hastj+4hatk find vec(PQ)

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

Find a unit vector in the diection of the vector. (i) (3hati + 4hatj - 5hatk) , (ii) (3hati - 2hatj + 6hatk) (iii) (hati + hatk) , (iv) (2hati + hatj + 2hatk)

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