you want to find $(x, y, z)$ so that it is orthogonal to $(1,0, 2)$ and $(3, -1, 0)$
that means $x + 2z = 0, 3x - y = 0$ if the basis of is more complex you will make a matrix made of these vectors as rows and row reduce them to solve for $x,y,z.$ in this example it is easier and we can set $z = -1$ and solve for $x = 2, y = 6$ so that $V^\perp$ is spanned  by $(2, 6, -1).$

the dimension of $W$ and $W^\perp$ should add up to the dimension of the space these are subspaces of.



edit: $\pmatrix{1&amp;0&amp;2&amp;|&amp;a\\3&amp;-1&amp;0&amp;|&amp;b} \rightarrow 
\pmatrix{1 &amp; 0 &amp; 2&amp;|&amp;a\\0&amp;-1&amp;-6&amp;|&amp;-3a + b}$

here $z$ is free variable and set it to $z = -1$. back substitution gives you $y = 6, x = 2$

if you had more than one free variable, you will set one of them to $1$ and the all rest to zero, then cycle through all of the free variables to get that many solutions in $W^\perp$

Orthogonal complement $V^\bot$ of the vector space $V=\langle(1,0,2),(3,-1,0)\rangle$ and $V\cap V^\bot$
I need to get the path of a specific font in my c:/windows/ folder 
The below code works perfectly when the target framework is 4.0
But my application can target only 3.5 and i need to use this in a console application c#

How can i achieve this ? Thanks.

string arialuniTff = path.Combine(System.Environment.GetFolderPath(System.Environment.SpecialFolder.Fonts), "arial.TTF");


Error Msg in 3.5 : 'System.Environment.SpecialFolder' does not contain a definition 
