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NDA 2021 Maths · Mathematics · Vector Algebra · medium

The point dividing the join of P(2hat i+3hat j-hat k) and Q(6hat i-hat j+3hat k) internally in the ratio 1:3 has position vector

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The point dividing the join of P(2i^+3j^−k^)P(2\hat i+3\hat j-\hat k) and Q(6i^−j^+3k^)Q(6\hat i-\hat j+3\hat k) internally in the ratio 1:31:3 has position vector
  1. A. 5i^+j^+2k^5\hat i+\hat j+2\hat k
  2. B. 4i^+j^+k^4\hat i+\hat j+\hat k
  3. C. 3i^+2j^3\hat i+2\hat j
  4. D. i^+2j^−k^\hat i+2\hat j-\hat k
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Answer: (C) 3i^+2j^3\hat i+2\hat j

For ratio m:n=1:3m:n=1:3 the position vector is nP⃗+mQ⃗m+n=3(2,3,−1)+(6,−1,3)4=(12,8,0)4=(3,2,0)\dfrac{n\vec P+m\vec Q}{m+n}=\dfrac{3(2,3,-1)+(6,-1,3)}{4}=\dfrac{(12,8,0)}{4}=(3,2,0). Swapping the weights (mm with nn) gives the ratio 3:13:1 point (5,0,2)(5,0,2), the usual trap.
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