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.

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 .

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 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

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

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.

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

If the position vector of the poinot A is a+2b and a point P with position vector vec(a) divides a line segement AB in the ratio 2:3 then the position vector of the point B is

If the position vector of a point (-4,\ -3)b e\ vec a ,\ find \ | vec a|dot

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

Show that the point A ,B ,C with position vectors vec a-2 vec b+3 vec c ,2 vec a+3 vec b-4 vec c and -7 vec b+10 vec c are collinear.