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