If →a and →b are the position vectors of →A and →B respectively, then find the position vector of point →C in −−→BA produced such that −−→BC=1.5−−→BA.
Since,−−→OA and −−→OB=→b∴ −−→BA=−−→OA−−−→OB=→a−→band 1.5−−→BA=1.5(→a−→b)Since, −−→BC=1.5→a−1.5→b−−→OC−−−→OB=1.5→a−0.5→b−−→OC=1.5→a−0.5→b+→b [∵ −−→OB=→b] =1.5→a−0.5→b =3→a−→b2
Graphically, explanation of the above solution is given below