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NDA 1 2024 Maths, question 66

Topic: Vectors

Q66Not scored: no correct option as printed

Let a→=i^−j^+k^\overrightarrow{a}=\hat{i}-\hat{j}+\hat{k} and b→=i^+2j^−k^\overrightarrow{b}=\hat{i}+2\hat{j}-\hat{k}. If a→×(b→×a→)=αi^−βj^+γk^\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{a})=\alpha\hat{i}-\beta\hat{j}+\gamma\hat{k}, then what is the value of α+β+γ\alpha+\beta+\gamma ?

  1. (a) 88
  2. (b) 77
  3. (c) 66
  4. (d) 11

Solution.

Not scored: no correct option as printed.

Answer: not scored. No option is correct as printed.

  1. The vector triple-product identity gives a × (b × a) = (a·a)b − (a·b)a.
  2. Here a·a = 3 and a·b = −2, so the result is 3b + 2a = (5, 4, −1).
  3. The printed right-hand side is αi − βj + γk, so α = 5, β = −4, γ = −1 and α + β + γ = 0.
  4. None of the four options equals 0.
  5. Replacing the printed minus before β by a plus would give 8, but that is an editorial repair, not the answer to the supplied question.