I'm trying to find out if a given vector say, $V_1$ ($i_1$, $j_1$, $k_1$) or $V_3$ ($i_3$, $j_3$, $k_3$) is pointing towards clockwise or anti clockwise direction around another vector $V_2$ ($i_2$, $j_2$, $k_2$) which is always perpendicular to it.
In the image linked below, the vector $V_2$ is the X-axis itself (the X-axis is pointing into the Y-Z plane), with the vectors $V_1$ and $V_3$ existing in the Y-Z plane.
In the image, we can visually see and figure using right hand rule that $V_1$ is anticlockwise and $V_3$ is clockwise ($V_2$ is going into the plane Y-Z, as mentioned before in above paragraph)