Find the position vector of a point `R` which divides the line joining the two points `P` and `Q` with position vectors `vec(OP)=2veca+vecb` and `vec(OQ)=veca-2vecb`, 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 (2\ vec a+ vec b) and ( vec a-\ 3 vec b) respectively, externally in the ratio 1:2.Also, show that P is the mid-point of the line segment R Qdot

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

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

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

The position vector of the point which divides the line segment joining the points with position vectors 2 vec(a) = 3b and vec(a) + vec(b) in the ratio 3:1 is

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 ratio 2:1.

The position vector of the point which divides the join of points 2veca-3vecbandveca+vecb in the ratio 3:1, is

Find the position vector of a point R which divides the line joining the point P(hati + 2hatj - hatk) and Q(-hati + hatj + hatk) in the ratio 2 : 1 internally .

Find the position vector of a point R which divides the line joining A(-2,1,3) and B(3,5,-2) in the ratio 2 : 1 (i) internally (ii) externally.

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