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

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Solution

The correct option is C

Let the line segment be AB, then as given
$A B c o s α = 3, A B c o s β = 4, A B c o s γ = 5$
$\Rightarrow A B^{2} (c o s^{2} α + c o s^{2} β + c o s^{2} γ) = 3^{2} + 4^{2} + 5^{2}$
$A B = \sqrt{9 + 16 + 25} = 5 \sqrt{2}$ ,
where $α$ , $β$ and $γ$ are the angles made by the line with the axes.

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

The correct option is C 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=5√2, where α, β and γ are the angles made by the line with the axes.