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Consider three vectors p → = i ^ + j ^ + k ^ ,   q → = 3 i ^ - j ^ + k ^ and r → = α i ^ + β j ^ + λ k ^ ,   ∀ α , β , λ ∈ R . If p → q → r → is maximum and r → = 2 6 , then the value of α - β - λ is equal to

Options

  1. A8
  2. B4
  3. C0
  4. D- 4

Correct answer

B. 4

Step-by-step solution

p → × q → = i ^ j ^ k ^ 1 1 1 3 - 1 1 = 2 i ^ + 2 j ^ - 4 k ^ For maximum p →   q →   r → , r → will be parallel to p → × q → So, r → = 2 μ i ^ + j ^ - 2 k ^   ∀ μ > 0 ⇒ μ = 1 (as r → = 2 6 ) ⇒ r → = 2 i ^ + 2 j ^ - 4 k ^ i.e. α = 2 ,   β = 2 ,   λ = - 4 Hence, α - β - λ = 2 - 2 + 4 = 4

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