HSC Arts 12th Board ExamMaharashtra State Board
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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 - HSC Arts 12th Board Exam - Mathematics and Statistics

#### 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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#### APPEARS IN

2015-2016 (March) (with solutions)
Question 1.2.3 | 2.00 marks

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Solution 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 Concept: Section formula.
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