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If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?

  1. θ = 30°
  2. θ = 45°
  3. 2 cos θ = 1
  4. 3 cos θ = 1

Answer (Detailed Solution Below)

Option 4 : 3 cos θ = 1
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Detailed Solution

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Concept:

 

Calculation:

 

 

Here, OA and BC are diagonals of cube 

O (0, 0, 0), A = (a, a, a), B = (0, 0, a), C = (a, a, 0)

Now,

 

 

Hence, option (4) is correct.

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