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AP EAMCET202120 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual

A ( 2 , 3 , 4 ) , B ( 4 , 5 , 7 ) , C ( 2 , - 6 , 3 ) , D ( 4 , - 4 , k ) are four points. If the line A B ¯ is parallel to C D ¯ then k is equal to

Options

  1. A2
  2. B4
  3. C5
  4. D6

Correct answer

D. 6

Step-by-step solution

A B → = 4 - 2 i ^ + 5 - 3 j ^ + 7 - 4 k ^ = 2 i ^ + 2 j ^ + 3 k ^ Direction ratios 2 , 2 , 3 C D → = 2 i ^ + 2 j ^ + ( k - 3 ) k ^ Direction ratios 2 , 2 , k - 3 For A B to be parallel to C D , the modulus of their direction cosines should be equal. Direction cosines of A B will be 2 17 , 2 17 , 3 17 And of C D will be 2 8 + k - 3 2 , 2 8 + k - 3 2 , k - 3 8 + k - 3 2 So, 2 17 = 2 8 + k - 3 2 ⇒ 17 = 8 + k - 3 2 ⇒ 9 = k 2 + 9 - 6 k ⇒ k k - 6 = 0 ⇒ k = 6

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