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NDA 2 2025 Maths, question 70

Topic: Vectors

Q70

A force F→=2i^−λj^+5k^\overrightarrow{F}=2\hat{i}-\lambda\hat{j}+5\hat{k} is applied at the point A(1,2,5)A(1,2,5). If its moment about the point B(−1,−2,3)B(-1,-2,3) is 16i^−6j^+2λk^16\hat{i}-6\hat{j}+2\lambda\hat{k}, then what is the value of λ\lambda?

  1. (a) −2-2Correct answer
  2. (b) 00
  3. (c) 11
  4. (d) 22

Solution.

Answer: (a) −2-2

  1. The position vector from B to A is r=(2,4,2).
  2. Hence r×F=(20+2λ,−6,−2λ−8).
  3. Matching its first component to 16 gives λ=−2; the third then becomes −4=2λ, independently confirming the result.