A point `C=(5veca+4vecb-5vecc)/3` divides the line joining the points `A` and `B= 2veca+3vecb-4vecc` in the ratio `2:1` then the position vector of `A` is

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

The line joining the points 6veca-4vecb+4vecc, -4vecc and the line joining the points -veca-2vecb-3vecc, veca+2vecb-5vecc intersect at

The line joining the points 6veca-4vecb+4vecc, -4vecc and the line joining the points -veca-2vecb-3vecc, veca+2vecb-5vecc intersect at

veca, vecb, vecc are the position vectors of the three points A,B,C respectiveluy. The point P divides the ilne segment AB internally in the ratio 2:1 and the point Q divides the lines segment BC externally in the ratio 3:2 show that 3vec)PQ) = -veca-8vecb+9vecc .

veca, vecb, vecc are the position vectors of the three points A,B,C respectiveluy. The point P divides the ilne segment AB internally in the ratio 2:1 and the point Q divides the lines segment BC externally in the ratio 3:2 show that 3vec(PQ) = -veca-8vecb+9vecc .

Show that the points veca+2vecb+3c-2veca+3vecb+5vecc and 7veca-vecc are colinear.

Show that the points veca+2vecb+3c,-2veca+3vecb+5vecc and 7veca-vecc are colinear.

Show that the three points veca-2vecb+3vecc, 2veca+3vecb-4vecc and -7vecb+10vecc are collinear.