Question

If projections of any line on coordinate axes are $3,4$ and $5$, then its length is:

• A. $12$
• B. $50$
• C. $5\sqrt{2}$
• D. $3\sqrt{2}$

Answer 1

Answer: (C)

$5\sqrt{2}$

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

$\Rightarrow d=5\sqrt{2}$