# Consider two points P and Q with position vectors and . Find the position vector of a point R which divides the line segment joining P and Q in the ratio 2:1,(i) Internally(ii) Externally(i) Internally

Given: and

To find: position vector of a point R which divides PQ in the ratio 2:1 internally

Formula used:

Position vector of a point B which divides AC in ratio of m:n internally is given by,

Therefore,

Here m = 2 and n = 1

(ii) Externally

Given: and

To find: position vector of a point R which divides PQ in the ratio 2:1 externally

Formula used:

Position vector of a point B which divides AC in the ratio of m:n externally is given by,

Therefore,

Here m = 2 and n = 1

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