L and M are two points with position vectors 2→a−→b and →a+2→b respectively. Write the position vector of a point N which divides the line segment LM in the ratio 2 : 1 externally.
Solution:
−−→OL=2→a−→b and −−→OM=→a+2→b Since N divides LM in 2:1 externally, so −−→ON=1.−−→OL−1.−−→OM1−1=2(2→a−→b)−(→a+2→b) Therefore, −−→ON=3→a−3→b