# Finding rotation matrix with respect to a given point in space.

I'm tasked with finding the matrix of a transformation $F$ such that it is a rotation with an angle $\theta$ with respect to the point (1,0,1).

I do not fully understand this as a rotation has only one angle. Does this mean I'm rotating on the axis defined by the vector (1,0,1)? When a problem like this comes up, usually what is it asking to do?

I've found some questions on here asking for help in similar problems (given a point, find the rotation with a given angle) but all I've found is in $\mathbb{R}^2$ and for that case I understand that you're meant to use a translation then rotate and then translate back. Is it something similar?

P.S If it helps, this is in a projective geometry course.

• A rotation around the vector $(1,0,1)$ looks the most plausible interpretation – G Cab May 17 '17 at 20:19
• Since you mentioned projective geometry, could the point be an element of the projective plane $\mathbb{RP}^2$ expressed in homogeneous coordinates? That would certainly make sense to me in that context. – amd May 18 '17 at 0:29
• This is also a thought I had, since the next exercise also has $z = 1$. I really dislike ambiguous instructions... – D. Brito May 18 '17 at 2:37
• @D.Brito If it is the task as interpreted by G Cab use the method described here math.stackexchange.com/questions/1599561/… – Widawensen May 18 '17 at 11:01