3d matrix rotation

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I've been reading up on rotation transformation and following this PowerPoint.

The assignment I'm working on is asking to perform a rotation and find the image $Q$ of the point P = (1, 2, -1) after a $45$ degree $y$-roll. I was under the impression that a roll was on the $z$-axis; which is where I'm confused.

I'm trying to set up the problem like such (from WikiPedia):

But I'm lost as to translate the 3 points into a matrix. Is this correct? The way I'm trying to visualize it as below without the translation.

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1 Answer

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To roll $\theta=\pi/4$ around the $y$ axis, the matrix becomes:

$$\begin{bmatrix}\sqrt{2}/2&0&\sqrt{2}/2\\0&1&0\\-\sqrt{2}/2&0&\sqrt{2}/2\end{bmatrix}$$

Applying this to the point:

$$\begin{bmatrix}\sqrt{2}/2&0&\sqrt{2}/2\\0&1&0\\-\sqrt{2}/2&0&\sqrt{2}/2\end{bmatrix}\begin{bmatrix}1\\2\\-1\end{bmatrix}=\begin{bmatrix}0\\2\\-\sqrt{2}\end{bmatrix}$$

So, $Q=(0,2,-\sqrt{2})$

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