If The Position Vector Of The Three Points Are ,  then The Three Points Are 

Let ABC be a triangle having its centroid at G. If S is any point in the plane of the triangle, then 

If O and O’ denote respectively the circum-centre and orthocentre of∆ABC, then 

If O and O’ denote respectively the circum-centre and orthocenter of âˆ†ABC, then  

Consider âˆ†ABC and ∆A₁B₁C₁ in such a way that  and M, N, M₁, N₁ be the mid-point of AB, BC, A₁B₁ and B₁C₁ respectively. Then,  

Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin, then  equals

If A, B, C, D be any four points and E and F be the middle points of AC and BD respectively, then  is equal to

Given that the vectors  are non-collinear, the values of x and yfor which the vector equality  holds true if  are  

Let  be three non-zero vectors, no two of which are collinear. If the vector  is collinear with  is collinear with  is equal to 

Three points with position vectors  will be collinear, if there exist scalars x, y, z such that