Consider two points P and Q with position vectors `vec(OP)=3hata-2vec(b)` and `vec(OQ)=vec(a)+vec(b)`. Find the position vector of a point R which divides the line joining P and Q in the ratio 2 : 1, (i) internally, and (ii) externally.

Consider two points P and Q with position vectors vec(OP)=3veca-2vecb and vec(OQ)=veca+vecb . Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1 , (i) intermally , and (ii) externally.

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.

P(2, -1, 4) and Q (4, 3, 2) are given points. Find the prove which divides the line joining P and Q in the ratio 2 : 3. (i) Internally (ii) Externally (Using vector method).

The position vector of the points A and B are respectively vec(a) and vec(b) . Find the position vectors of the points which divide AB in trisection.

Find the position vectors of the points which divide the join of the points 2 vec a-3 vec ba n d3 vec a-2 vec b internally and externally in the ratio 2:3 .

Find the position vector of the mid point of the vector joining the points P(2,3,4) and Q(4,1,-2).

Position vector of a point vec(P) is a vector whose initial point is origin.

If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are hati+2hatj-hatk and -hati+hatj+hatk respectively, in the ratio 2 : 1. (i) internally (ii) externally