Question

The projection of a line segment having length $13cm$ on $xy,yz$ planes are $5,4\sqrt{10}$ respectively. The projection of a line segment on $xz$ plane is

• A. $\sqrt{133}$
• B. $\sqrt{153}$
• C. $\sqrt{33}$
• D. $\sqrt{121}$

Answer 1

The correct option is A $\sqrt{133}$

Let the line segment be $x\hat{i}+y\hat{j}+z\hat{k}.$

Its length is $13cm$

$\Rightarrow =\sqrt{(x-0{)}^2+(y-0{)}^2+(z-0{)}^2}=13\Rightarrow x^2+y^2+z^2=169$ (1)

Its projection of $xy$ plane is $5$

As z - coordinates is zero on xy plane,

$\sqrt{x^2+y^2}=5\Rightarrow x^2+y^2=25$ (2)

Similarly on yz plane,

$\sqrt{Y^2+z^2}=4\sqrt{1}0\Rightarrow y^2+z^2=160$ (3)

Putting (3) in (1), we get,

$x^2+160=169\Rightarrow x^2=9\therefore x=3$

Putting $x$ value in (2), we get,

$9+y^2=25$

$\therefore y=4$

Putting y value in (3), we get,

$16+z^2=160$

$\therefore z=12$

Therefore, projection of xz plane is $\sqrt{x^2+x^2}$

$=\sqrt{3^2+{12}^2}$

$=\sqrt{153}$

Hence the answer is $\sqrt{153}$