The position vectors of four points P,Q,R annd S are 2a+4c,5a+`3sqrt(3)b+4c,-2sqrt(3)b+c and 2a+c` respectively, prove that PQ is parallel to RS.

If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

The position vectors of the points A,B and C are hati+2hatj-hatk,hati+hatj+hatk and 2hati+3hatj+2hatk , respectively. If A is chosen as the origin, then the position vectors of B and C are

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

The position vectors of two points A and B are respectively 6vec(a)+2vec(b) and vec(a)-3bar(b) . If the point C divides AB internally in the ratio 3 : 2 then the position vector of C is ……………

Consider two points P and Q with position vectors 2vec(a)+vec(b) and vec(a)-3vec(b) respectively. Find the position vector of a point R which divide the line segment joining P and Q in the ratio. 1 : 2 externally. Prove that P is a midpoint of line segment RQ.

A,B,C and D have position vectors a,b,c and d, respectively, such that a-b=2(d-c). Then,

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

If three points A,B and C have position vectors (1,x,3),(3,4,7) and (y,-2,-5), respectively and if they are collinear, then find (x,y).

The position vector of a point C with respect to B is hat i +hat j and that of B with respect to A is hati-hatj . The position vector of C with respect to A is

The points with coordinates (2a,3a), (3b,2b) and (c,c) are collinear