If A and B are two points whose position vectors are `3hati+2hatj-2hatk` and `hati-3hatj-hatk` respectively. Find the position vectors of the points dividing the segment AB
internally in the ratio 1:3.

If A and B are two points whose position vectors are 3hati+2hatj-2hatk and hati-3hatj-hatk respectively. Find the position vectors of the points dividing the segment AB externally in the ratio 3:1.

The position vectors of A and B are 2hati-9hatj-4hatk and 6hati-3hatj+8hatk respectively, then the magnitude of AB is

The position vectors of A and B are hati-hatj+2hatk and 3hati-hatj+3hatk . The position vector of the middle points of the line AB is

If three points A,B and C are collinear, whose position vectors are hati-2hatj-8hatk,5hati-2hatk and 11hati+3hatj+7hatk respectively, then the ratio in which B divides AC is

If the position vectors of the points A and B are hati+3hatj-hatk and 3hati-hatj-3hatk , then what will be the position vector of the mid-point of AB

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

Two unlike forces of equal magnitudes hatj+2hatk and -hatj-2hatk are acting at the points whose position vectors are given by hati+hatj+hatk and hati+2hatj+3hatk respectively. Find the moment of the couple formed by these forces.

If the position vectors of A and B are hati+3hatj-7hatk and 5hati-2hatj+4hatk , then the direction cosine of AB along Y-axis is

A line passes through the points whose position vectors are hati+hatj-2hatk and hati-3hatj+hatk . The position vector of a point on it at unit distance from the first point is (A) (1)/(5)(5hati+hatj-7hatk) (B) (1)/(5)(5hati+9hatj-13hatk) (C) (hati-4hatj+3hatk) (D) (1)/(5)(hati-4hatj+3hatk)