Find the projection matrix that projects every vector of $\mathbb{R}^3$ on to the plane of 2 vectors The two vectors that are mentioned above are $$\begin{pmatrix}1 \\1 \\0\end{pmatrix}$$ $$\begin{pmatrix}0 \\ 1 \\1 \end{pmatrix}$$
I am not really sure what i am doing but i tried finding the projection matrix by putting the 2 vectors into a different matrix A =$$\begin{pmatrix}1 & 0 \\1 &1 \\0&1\end{pmatrix}$$ and then calclulating the projection matrix $$ P = A (A^TA)^{-1} A^T$$
.My result is that the P matrix is $$ 1/2\begin{pmatrix}1/2 & 1 & -1\\1&2&1\\-1 & 1 &2\end{pmatrix}$$
Is my answer correct? If not what am i doing wrong? Thanks in advance

Your answer is not correct, as can be seen by checking $P\begin{pmatrix}1\\1\\0\end{pmatrix}$.  
Here's a suggestion how to find such a projection matrix easily.  Use the standard basis for $\mathbb R^3$.  
The columns of the matrix are the images of the basis vectors.  
For example, the following matrix will map all vectors in $\mathbb R^3$ 
to the plane spanned by $\begin{pmatrix}1\\1\\0\end{pmatrix}$ and $\begin{pmatrix}0\\1\\1\end{pmatrix},$ because it maps the standard basis vectors there:
$\begin{pmatrix}1 & 0 &0 \\ 1 &1 &1 \\ 0 &1 &1 \end{pmatrix}.$  As long as the columns are vectors in the plane spanned by $\begin{pmatrix}1\\1\\0\end{pmatrix}$ and $\begin{pmatrix}0\\1\\1\end{pmatrix},$ 
the image will be in that plane.
