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NDA 2025 Maths · Mathematics · Vector Algebra · easy

The position vector of the midpoint of the segment joining A(2,3,1) and B(4,-1,3) is

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The position vector of the midpoint of the segment joining A(2,3,1)A(2,3,1) and B(4,−1,3)B(4,-1,3) is
  1. A. 6i^+2j^+4k^6\hat i+2\hat j+4\hat k
  2. B. 3i^+j^+2k^3\hat i+\hat j+2\hat k
  3. C. i^+2j^+k^\hat i+2\hat j+\hat k
  4. D. 3i^+2j^+k^3\hat i+2\hat j+\hat k
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Answer: (B) 3i^+j^+2k^3\hat i+\hat j+2\hat k

The midpoint has position vector a⃗+b⃗2=(2+4)i^+(3−1)j^+(1+3)k^2=3i^+j^+2k^\frac{\vec a+\vec b}{2}=\frac{(2+4)\hat i+(3-1)\hat j+(1+3)\hat k}{2}=3\hat i+\hat j+2\hat k. The option 6i^+2j^+4k^6\hat i+2\hat j+4\hat k is the sum with no halving, and i^+2j^+k^\hat i+2\hat j+\hat k is half the difference b⃗−a⃗2\frac{\vec b-\vec a}{2}.
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