Question

The projection of any line on co-ordinate axes be respectively 3, 4, 5 then its length is

• A. 12
• B. 50
• C. $5\sqrt{2}$
• D. 25

Answer 1

The correct option is C $5\sqrt{2}$

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