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Paragraph: Let S be the line of intersection of two planes x+y+z=1 and 2 x+3 y-4 z=8 . Question: If (l, m, n) are direction cosines of S, then what is the value of 43 (l^2-m^2-n^2 ) ?

Options

  1. A6
  2. B5
  3. C4
  4. D1

Correct answer

A. 6

Step-by-step solution

2 planes are x+y+z=1 and 2 x+3 y-4 z=8 . DC 's of line: S are 1, ~m , n aligned & 1= -7 86 , m= 6 86 , n= 1 86 & 43 (1^2-m^2-n^2 )=43 ( 49 86 - 36 86 - 1 86 )=43 12 86 =6 aligned

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