At $\mathbb{R}^2$, we rotate a point (or a vector) $v = \left( v_1 , v_2 \right) \in \mathbb{R}^2$ around a point, by a angle. For example: the rotation of $(1,0)$ around the origin $(0,0)$ by a angle of $\frac{\pi}{2}$, anticlockwise, is the point (or the vector) $\left( 0,1 \right)$.
At $\mathbb{R}^3$ we can rotate a point, by a angle, but now around a line, with a similar process at $\mathbb{R}^2$.
My question is: at $\mathbb{R}^4$, we rotate a point around a plane? And at $\mathbb{R}^1 = \mathbb{R}$, what is a "rotation" in this space?