Maharashtra State BoardHSC Arts 12th Board Exam
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If p=i−2j+k and q=i+4j+2k 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 - Mathematics and Statistics

Sum

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

 
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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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