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KCET2021MathematicsThree Dimensional Geometry

The angle between the lines whose direction cosines are ( 3 4 , 1 4 , 3 2 ) and ( 3 4 , 1 4 , - 3 2 ) is

Options

  1. A2
  2. B3
  3. C4

Correct answer

C. 4

Step-by-step solution

Given, direction cosines of line 1: (l₁, m₁, n₁ )= ( 3 4 , 1 4 , 3 2 ) direction cosines of line 2 (l₂, m₂, n₂ )= ( 3 4 , 1 4 ,- 3 2 ) We know that, angle between two lines is given by = |l₁ l₂+m₁ m₂+n₁ n₂ | aligned &= | 3 4 3 4 + 1 4 1 4 - 3 2 3 2 | &= | 3 16 + 1 16 - 3 4 |= | 3+1-12 16 | &= |- 8 16 |= 1 2 &= 3 aligned

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