Q. 84.2( 5 Votes )

# 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

Answer :

**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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If is a unit vector and then find

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