Find the position vector of a point which divides the join of points with position vectors ` vec a-2 vec b` and `2 vec a+ vec b` externally in the ration 2:1.

Find the position vector of the point, which divides the join of points with position vectors 3vec(a)-2vec(b) and 2vec(a)+3vec(b) in the ratio 2 : 1.

Find the position vector of a point R which divides the line segment joining P and Q whose position vectors are 2vec a+vec b and vec a-4vec b ,externally in the ratio 1:2, also show that P is the midpoint of the line segment RQ.

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

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors vec OP=2vec a+vec b and vec OQ=vec a-2vec b, respectively in the ratio 1:2 internally and externally.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2vec a+vec b) and (vec a-3vec b) respectively,externally in the ratio 1:2. Also,show that P is the mid-point of the line segment RQ.

Write the position vector of a point dividing the line segment joining points A and B with position vectors vec a and vec b externally in the ration 1:4 where vec a=2hat i+3hat j+4hat k and vec b=-hat i+hat j+hat k

The position vector of the point which divides the join of points 2vec(a)-3vec(b) and vec(a)+vec(b) in the ratio 3:1 is

Find the position vector of R, which divides the line joining two points P(2vec(a)+vec(b)) and Q(vec(a)-3vec(b)) externally in the ratio 1 : 2. Also show that P is the middle point of the segment RQ.

The position vector of a midpoint lying on the line joining the points whose position vectors are vec i+vec j-vec k and vec i-vec j+vec k is

If the position vector of a point (-4,-3) be vec a, find |a|