Section formula:

Internal division:

Let A and B be 2 points with position vectors  and  respectively, and C be a point which is dividing AB internally in ratio m: n. Then the position vector of C can be given by .

Proof: Let O be origin. The , let  be the position vector of C which divides AB internally in ratio m : n then,                                                 AB/CB = m/n

External division:

Let A and B be 2 points with position vectors  and  respectively and let C be a point dividing  externally in ratio m : n. Then position vector of  can be given by. 

Note: 

(i) If C is mid-point of AB, then P.V. of C is .

(ii) We have,. Thus is in the form of . here, 

 .Thus, position vector of any point  on  can always be taken as  where .

(iii) If circumcentre is origin and the vertices of triangle have position vectors, then position vector of orthocentre will be -(+ + ).

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