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Question
If `bar p = hat i - 2 hat j + hat k and bar q = hat i + 4 hat j - 2 hat k` are position vector (P.V.) of points P and Q, find the position vector of the point R which divides segment PQ internally in the ratio 2:1
Solution 1
R is the point which divides the line segment joining the points PQ internally in the ratio 2:1.
`bar r=(2(bar q)+1(bar p))/(2+1)`
`=(2(hati+4hatj-2hatk)+1(hati-2hatj+hatk))/(3)`
`=(3hati+6hatj-3hatk)/3`
`barr=hati+2hatj-hatk`
The position vector of point R is `hati+2hatj-hatk`
Solution 2
Position vector of point R in
`vec(OR)=(vec(OQ)xx2+1xxvec(OP))/(2+1)`
`vec(OR)=(2(hati+4hatj-2hatk)+1(hati-2hatj+hatk))/3`
`vec(OR)=(2hati+8hatj-4hatk+hati-2hatj+hatk)/3`
`vec(OR)=(3hati+6hatj-3hatk)/3`
`vec(OR)=hati+2hatj-hatk`
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