Example 11 - Chapter 11 Class 12 - Find shortest distance - Shortest distance between two skew lines

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  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise

Transcript

Example 11 Find the shortest distance between the lines l1 and l2 whose vector equations are = + + (2 + ) and = 2 + + (3 5 + 2 ) Shortest distance between lines with vector equations = 1 + 1 and = 2 + 2 is 1 2 . 2 1 1 2 Given, Now = (2 + 1 1 ) (1 + 1 + 0 ) = (2 1) + (1 1) + ( 1 0) = 1 + 0 1 = 2 1 1 3 5 2 = 1 2 ( 5 1) 2 2 ( 3 1) + 2 5 (3 1) = 2+5 4 3 + 10+3 = (3) (1) + ( 7) = 3 7 Magnitude of ( 1 2 ) = 32+ 1 2+ 7 2 = 9+1+49 = Also, ( ) .( ) = (3 7 ) . (1 + 0 1 ) = (3 1) + ( 1 0) + ( 7 1) = 3 + 0 + 7 = 10 Shortest distance = 1 2 . 2 1 1 2 = 10 59 = Therefore the shortest distance between the given lines is 10 59 .

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