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Question

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are ^i+2^j^k and ^i+^j+^k respectively, in the ratio 2:1
externally.

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Solution

The position vector of a point R divided the line segment joining two points P and Q in the ratio m : n is given by
Case I Internally= mb+nam+n
Case II Externally=mbnamn
Position vectors of P and Q are given as
OP=^i+2^j^k and OQ=^i+^j+^k
PV of R [dividing (PQ) in the ratio 2 : 1 externally]
=m(PV of Q)n(PV of P)mn, here m=2, n=1=2(PV of Q)1(PV of P)21
=2(^i+^j+^k)+(1)(^i+2^j^k)=(3)^i+0^j+3^k=3^i+3^k


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