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Let the volume of a parallelepiped whose coterminous edges are given by u → = i ^ + j ^ + λ k ^ , v → = i ^ + j ^ + 3 k ^ and w → = 2 i ^ + j ^ + k ^ be 1 cu. unit. If θ be the angle between the edges u → and w → , then the value of cos ⁡ θ can be

Options

  1. A7 6 6
  2. B7 6 3
  3. C5 7
  4. D5 3 3

Correct answer

B. 7 6 3

Step-by-step solution

± 1 = 1 1 λ 1 1 3 2 1 1 ⇒ = - λ + 3 = ± 1 ⇒ λ = 2 o r λ = 4 For λ = 4 c o s θ = 2 + 1 + 4 6 18 = 7 6 3

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