Consider two points A and B with position vectors `vec(OA)=veca-4vecb` and `vec(OB)=veca-vecb`.Find the position vector of a point R which divides the line joining A and B in the ratio 2:1 internally

Consider two points P and Q with position vectors vec(OP)=3 veca-2 vecb 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) Internally and ii) externally.

Find the position vector of a point R which divides the line joining the points P and Q whose vectors i+2j-k and -i+j+k in the ratio 2:1 externally.

Find the position vector of a point R which divides the line joining the points P and Q whose vectors are i+2j-k and -i+j+k in the ratio 2:1 Internally.

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

Consider the point A(2,1,1) and B(4,2,3) Find the vector vec(ab)

The point which divides the line joining the points (1,3,4) and (4,3,1) internally in the ratio 2:1 , is

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

Consider the points P (3,4,-5) and Q (1,-2,3).Find the co-ordinates of the point which divides the join of P and Q in the ratio a)1:2 internally b)3:2 externally

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

Consider the following figure (b)Find the co-ordinates of the point which divides the line segemnt joining the points P and Q internally in the ratio 2:3.