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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, externally in 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 externally 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)`
`= -3hati + 0hatj + 3hatk`
`= -3hati + 3hatk`.
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