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AP EAMCET2014MathematicsThree Dimensional Geometry

If A(3,4,5), B(4,6,3), C(-1,2,4) and D(1,0,5) are such that the angle between the lines D C and A B is , then is equal to

Options

  1. A7 9
  2. B2 9
  3. C4 9
  4. D5 9

Correct answer

C. 4 9

Step-by-step solution

Given points are A(3,4,5), B(4,6,3), C(-1,2,4) and D(1,0,5) . Now DR's of D C=(-2,2,-1) DR's of A B=(1,2,-2) Let, be the angle between A B and D C . aligned & = a₁ a₂+b₁ b₂+c₁ c₂ a₁^2+b₁^2+c₁^2 a₂^2+b₂^2+c₂^2 = & -2 1+2 2-1 (-2) (-2)^2+(2)^2+(-1)^2 (1)^2+(2)^2+(-2)^2 & = -2+4+2 4+4+1 1+4+4 = 4 3 3 = 4 9 aligned

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