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NCERT Class 12 · Ch 10 Miscellaneous Exercise · Q9

NCERT Class 12 Maths · Chapter 10 Vector Algebra · Miscellaneous Exercise Question 9

P,Q have position vectors 2a+b and a−3b. Find R dividing PQ externally in ratio 1:2, and show P is the midpoint of RQ.

💡 Concept Hints

  1. Write the vector components and identify the required direction or geometric relation.
  2. Use the magnitude, dot-product, cross-product or section formula that matches the requested quantity.

✅ Step-by-Step Solution

Final Answer: R=3a+5b.
  1. The external section formula gives R=[1Q−2P]/(1−2)=2P−Q=2(2a+b)−(a−3b)=3a+5b.
  2. Then (R+Q)/2=[(3a+5b)+(a−3b)]/2=2a+b=P, proving the midpoint claim.

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