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AP EAMCET201921 Apr 2019Evening ShiftMathematicsThree Dimensional GeometryActual

The angle between a line with direction ratios 2 , 2 , 1 and the line joining the points ( 3 , 1 , 4 ) and ( 7 , 2 , 12 ) is

Options

  1. Acos - 1 2 3
  2. Bcos - 1 3 4
  3. Ctan - 1 - 2 3
  4. Dcos - 1 1 3

Correct answer

A. cos - 1 2 3

Step-by-step solution

It is given that the direction ratios of first-line are   2 , 2 , 1 and the direction ratios of second-line joining the points ( 3 , 1 , 4 ) and ( 7 , 2 , 12 ) are, ( 7 - 3 , 2 - 1 , 12 - 4 ) ( 4 , 1 , 8 ) The angle between the two lines is, cos θ = a 1 a 2 + b 1 b 2 + c 1 c 2 a 1 2 + b 1 2 + c 1 2 a 2 2 + b 2 2 + c 2 2 cos θ = 2 × 4 + 2 × 1 + 1 × 8 9 81 = 18 27 θ = cos - 1 2 3

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