Projecting vectors onto line (finding matrix associated with transformation)

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Find the matrix associated with the transformation that projects vectors in $\mathbb{R^3}$ orthogonally onto the line with parametric equations x=t, y=0, z=t. Find using rotations and projections. enter image description here

Thoughts: I know that the direction vector of the line given is $<1,0,1>$. I want to project vectors in $\mathbb{R^3}$ orthogonally onto this line. I know there is some formula where you just plug in different vectors and get the final matrix. However, I do not want do not want to get the answer like this, although I know it can be done.

I want to do this by rotations. I was thinking that I have to first multiply by a rotation matrix (rotating vectors), then project onto the XY plane (and multiply by this matrix), and then multiply by the transpose of the first rotation matrix to rotate back. The product of these matrices I was thinking should give the matrix associated with the transformation that projects vectors orthogonally onto the line.
However, I'm not sure if this is entirely the correct process and what exactly the first rotation matrix should be for the first one (that is, by what degrees and in which direction).

Any help would be much appreciated, thank you.