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NDA 2019 Maths · Mathematics · Vector Algebra · easy

The points P and Q have position vectors hat i+2hat j and 3hat i-2hat j. The point R divides PQ externally in the ratio 3:1. The position vector of R…

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The points PP and QQ have position vectors i^+2j^\hat i+2\hat j and 3i^−2j^3\hat i-2\hat j. The point RR divides PQPQ externally in the ratio 3:13:1. The position vector of RR is
  1. A. 52i^−j^\frac52\hat i-\hat j
  2. B. 5i^−j^5\hat i-\hat j
  3. C. 2i^+2j^2\hat i+2\hat j
  4. D. 4i^−4j^4\hat i-4\hat j
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Answer: (D) 4i^−4j^4\hat i-4\hat j

For external division in the ratio m:nm:n, r⃗=mq⃗−np⃗m−n=3(3i^−2j^)−(i^+2j^)2=8i^−8j^2=4i^−4j^\vec r=\frac{m\vec q-n\vec p}{m-n}=\frac{3(3\hat i-2\hat j)-(\hat i+2\hat j)}{2}=\frac{8\hat i-8\hat j}{2}=4\hat i-4\hat j. The internal division would give 3q⃗+p⃗4=52i^−j^\frac{3\vec q+\vec p}{4}=\frac52\hat i-\hat j, the first distractor.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake