Section Formula Co-ordinate Geometry Theorem

Section formula co-ordinate geometry is commonly used in vector algebra. This theorem is applied for the derivation of position vector of a point that divides a line internally.

Section Formula Theorem Derivation , Proof

The position vector of the point that divides internally the line joining two points whose position vectors are
in the given ratio m:n is

Let O be the origin of vectors.
Let A and B be the two given points whose position vectors with respect to O are and respectively.

Let P be the point on AB which divides AB internally in the ratio m:n. Let the position vector be

Hence the Section Formula Co-ordinate Geometry theorem is proved with the above derivation, proof.

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