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MHT CET2011MathematicsThree Dimensional Geometry

The angle between a line with direction ratio 2: 2: 1 and a line joining (3,1,4) to (7,2,12) is

Options

  1. A⁻¹(2 / 3)
  2. B⁻¹(3 / 2)
  3. C⁻¹(-2 / 3)
  4. DNone of the above

Correct answer

A. ⁻¹(2 / 3)

Step-by-step solution

Direction ratios of the line joining the points (3,1,4) and (7,2,12) are array l = 7-3,2-1,12-4 = = a₁, a₂, a₃ array And the direction ratio of given line is array l = = array Let Q be the angle between the lines, then = a₁ b₁+a₂ b₂+a₃ b₃ a₁²+a₂²+a₃² b₁²+b₂²+b₃² array l = (4)(2)+(1)(2)+(8)(1) 16+1+64 4+4+1 = 18 81 9 = 18 9 3 = 2 3 = ⁻¹ ( 2 3 ) array

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