Question

The projection of any line on coordinate to the respectively $3,4$ and $5$, then its length is

• A. $50$
• B. $12$
• C. $5\sqrt{2}$
• D. none of these

Answer 1

The correct option is C

$5\sqrt{2}$

Explanation for correct option:

Let the length of line $=d$ ,

then projection on $x-$axis, $l=3$ ,

projection on $y-$axis, $m=4$,

projection on $z-$axis, $n=5$

$$\begin{gathered} \Rightarrow d^2=l^2+m^2+n^2 \\ \Rightarrow d^2=3^2+4^2+5 \\ \Rightarrow d^2=9+16+25 \\ \Rightarrow d=\sqrt{50} \\ \Rightarrow d=5\sqrt{2} \end{gathered}$$

Hence, option (C), $5\sqrt{2}$ is the correct answer.