Torque is analog of force in rotational motion and it has one of two directions I.e clockwise and counterclockwise . How I can visualise these directions . For example r and F are on same plane(x and y axes) then according to righthand rule torque will be on z axis but I find it difficult to visualise .
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Torque by being the (external) product of the force applied by the radius of application represents an axial vector (or rotational vector)
$$\vec{T} = \vec{F} \times \vec{r}$$
One way to represent such vector (related to the definition above) is a by a vector which is perpendicular to the plane generated by both $\vec{F}$ and $\vec{r}$ and which has a magnitude equalt to the rotational torque.
Whether the torque vector $\vec{T}$ points "upward" from this plane or "downward" is related to whether the rotation is clock-wise or counter-clockwise (any convention will do as long as it is consistent).
See diagram below for visual:
Nikos M.
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The vectors representing physical quantities relating to a rotating object or system are chosen to be along the axis of rotation because that is the only direction which is not continuously changing. The right hand rule was an arbitrary choice.
R.W. Bird
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