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NDA 2023 Maths · Mathematics · Vector Algebra · medium

If A and B have position vectors vec a and vec b, the position vector of the point dividing AB externally in the ratio 3:1 is

Single correct option

If AA and BB have position vectors a⃗\vec a and b⃗\vec b, the position vector of the point dividing ABAB externally in the ratio 3:13:1 is
  1. A. 3b⃗+a⃗4\dfrac{3\vec b+\vec a}{4}
  2. B. 3b⃗−a⃗2\dfrac{3\vec b-\vec a}{2}
  3. C. a⃗+3b⃗2\dfrac{\vec a+3\vec b}{2}
  4. D. b⃗−3a⃗2\dfrac{\vec b-3\vec a}{2}
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Answer: (B) 3b⃗−a⃗2\dfrac{3\vec b-\vec a}{2}

For external division in ratio m:nm:n the point is mb⃗−na⃗m−n=3b⃗−a⃗2\dfrac{m\vec b-n\vec a}{m-n}=\dfrac{3\vec b-\vec a}{2}. The option 3b⃗+a⃗4\dfrac{3\vec b+\vec a}{4} is the internal division formula.
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Original question written in the NDA 2023 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