Collinear Vectors Vectors a and b are collinear , if a = λb , for some non-zero scalar λ .
Collinear Points Let A , B , C be any three points . Points A , B , C are collinear <=> AB , BC are collinear vectors . <=> AB = λBC for some non-zero scalar λ .
Section Formula
Let A and B be two points with position vectors a and b , respectively and OP = r .
( i ) Let P be a point dividing AB internally in the
ratio m : n . Then , r = m b + n a / m + n
Also , ( m + n ) OP = m OB + n OA
( ii ) The position vector of the mid-point of a and b is a + b / 2 . ( iii ) Let P be a point dividing AB externally in the
ratio m : n . Then , r = m b + n a / m + n
Position Vector of Different Centre of a Triangle
( i ) If a , b , c be PV ’ s of the vertices A , B , C of a ΔABC respectively , then the PV of the centroid
G of the triangle is a + b + c / 3 .
( ii ) The PV of incentre of ΔABC is ( BC ) a + ( CA ) b + ( AB ) c / BC + CA + AB The PV of orthocentre of ΔABC is
a ( tan A ) + b ( tan B ) + c ( tan C ) / tan A + tan B + tan C