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KCET2018MathematicsThree Dimensional Geometry

The angle between the lines ( 2 x=3 y=-z ) and ( 6 x=-y=-4 z ) is

Options

  1. A( 0^ )
  2. B( 45^ )
  3. C( 90^ )
  4. D( 30^ )

Correct answer

C. ( 90^ )

Step-by-step solution

Given lines, 2 x=3 y=-z x 1 / 2 = y 1 / 3 = z -1 (1) Direction ratios are (1 / 2,1 / 3,-1) and 6 x=-y=-4 z x 1 / 6 = y -1 = z -1 / 4 (2) Direction ratios are (1 / 6,-1,-1 / 4) Now, l₁ l₂+m₁ m₂+n₁ n₂ 1 12 - 1 3 + 1 4 = 1-4+3 12 =0 Therefore, lines are perpendicular, that is, angle between two lines is 90^ .

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