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99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

If A ( a → ) , B ( b → ) , C ( c → ) and D ( d → ) are four points such that a → = - 2 i ^ + 4 j ^ + 3 k ^ , b → = 2 i ^ - 8 j ^ , c → = i ^ - 3 j ^ + 5 k ^ and d → = 4 i ^ + j ^ - 7 k ^ and d 1 is the shortest distance between the lines A B and C D , then which of the following is true:

Options

  1. Ad 1 = 0, hence AB and CD intersect
  2. BAB and CD are skew lines and d 1 = 20 13
  3. CAB and CD are skew-lines and d 1 = 23 13
  4. DAB and CD are skew lines and d 1 = 25 13

Correct answer

C. AB and CD are skew-lines and d 1 = 23 13

Step-by-step solution

A B → = 4 i ^ - 12 j ^ - 3 k ^ C D → = 3 i ^ + 4 j ^ - 12 k ^ A C → = 3 i ^ - 7 j ^ + 2 k ^ B D → = 2 i ^ + 9 j ^ - 7 k ^ ∴ d 1 = A B → × C D → . A C → A B → × C D → = A B → × C D → . B D → A B → × C D → ∴ d 1 = 23 13

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