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  4. If projection of any line on coordinate axes 3, 4 and 5, then its length is

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Q. If projection of any line on coordinate axes $3, 4$ and $5$, then its length is

BITSATBITSAT 2011

Solution:

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