Write the expression for torque in vector form.

Hint: The concept of the electrical moment can define the direction concept of torque alright. Torque or moment of force may be a rotational force that has the tendency to rotate the body on which it's applied, a bit like a linear force may be a push or a pull, a torque is often considered as a twist to an object.
It is a vector quantity.

Complete step-by-step solution:
In vector form, torque is the vector product of the radius vector (from the axis of rotation to the point of application of force) and therefore the force vector.
A particle is found at position r relative to its axis of rotation. When a force F is applied to the particle, the perpendicular component F produces a torque.
An electric dipole is an appointment of opposite amounts that's adequate to electric charges, separated by fixed distance for this the condition is that the amount is going to be different which's positive and negative.
Electric Dipole Moment: It is often defined because of the separation between the positive and therefore the negative electrical charges within a system. By this one can measure the general polarity of the system. The SI Unit of the electrical moment is coulomb meter (cm) which is understood as Debye (D) which is additionally a vector sort of torque. When any physical quantity has direction and magnitude it's called a vector. In electricity when two currents meet at a function, the resultant current of those is going to be a resultant.
In vector form, the cross product of the radius vector and the force vector produces Torque.
\[\overrightarrow \tau = \overrightarrow r \times \overrightarrow F \]
When torque is the cross product of lever radius r and force F,
\[\overrightarrow \tau = \left| {\overrightarrow r } \right| \times \overrightarrow {\left| F \right|} \sin \theta \]
It’s the product of force and its perpendicular distance from the lever’s fulcrum
So from above,
\[\overrightarrow \tau \times \overrightarrow F = \left| {\overrightarrow r } \right| \times \overrightarrow {\left| a \right|} \sin \theta \]
SI Unit of Torque is Newton meter.
Electric field lines are visualizing vector fields, they need a pattern of lines mentioned as field lines.
These lines are directed far away from the positive source to negative source change in a curve drawn in such a way that the tangent of it at each point is in the direction of the internet field.

Note: In 3-dimensions, the torque is a false vector for point particles. Electric Field near the change is high and when we go further it decreases because the electric field is inversely proportional to the square of the distance.