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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 `hati + 2hatj - hatk` and `-hati + hatj + hatk` respectively, internally the ratio 2:1.
Solution
Here `veca = hati + 2hatj - hatk` and `vecb = hat-i + hatj + hatk`
The position vector of R, dividing the join of P and Q internally in the ratio 2:1 is
`vecR = (mvecb + nveca)/(m + n)`
`= (2 (vecb) + 1 (veca))/(2 + 1)`
`= (2 (- hati + hatj + hatk) + 1(hati + 2hatj - hatk))/ (2 + 1)`
`= (-1)/3 hati + 4/3 hatj + 1/3hatk.`
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