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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
(i) Internally (ii) externally

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Solution

a=^i+2^j^kb=^i+^j+^k
Position vector of a point for internal division mb+nam+n=2(^i+^j+^k)+1(^i+2^j^k)2+1=^i+4^j+^k3
Position vector of a point for external division
mb+namn=3^i+3^k21=3^i+3^k

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