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Question

The projection of any line on co-ordinate axes be respectively 3, 4, 5 then its length is [MP PET 1995; RPET 2001]


  1. None of these

  2. 50

  3. 12


Solution

The correct option is A


Let the line segment be AB, then as given
AB cos α=3,AB cos β=4,AB cos γ=5
AB2(cos2 α+cos2 β+cos2 γ)=32+42+52
AB=9+16+25=52,
where α, β and γ are the angles made by the line with the axes.

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