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 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 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.

Find the coordinates of a point which divides externally the line joining (1, -3) and (-3, 9) in the ratio 1 : 3.

Find the coordinates of the point which divides the line segment joining the points (1, -2, 3) and (3, 4, -5) in the ratio 2 : 3 (i) internally, and (ii) externally.

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 coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.

Find the coordinates of the point which divides the line segment joining the points (-1, 7) and (4, -3) in the ratio 2:3 .

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 .