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  4. The projection of any line on coordinate axes be respectively 3, 4, 5, then its length is:

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Q. The projection of any line on coordinate axes be respectively $ 3, 4, 5, $ then its length is:

Jharkhand CECEJharkhand CECE 2003

Solution:

Let $d$ be the length of line, then projection on $x$-axis $= dl = 3$,
projection of $y$-axis $= dm = 4$
and projection on $z$-axis $= dn = 5$
$d^{2}\left(l^{2}+m^{2}+n^{2}\right)=50$
$\Rightarrow d^{2}=50$
$\Rightarrow d=5 \sqrt{2}$