Like in this figure we see that the surface molecules have a net downward force to all of these so should any force which we made along a line on the surface the force be downwards ? Why the surface tension is parallel to the surface ? 
Why surface tension direction cannot be downwards in direction when considered the surface of fluid?
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Orion_Pax
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The existence of a surface with unsatisfied bonds produces an energy penalty. This results in an internal Laplace pressure, an increase in the chemical potential of the system, and a resistance to increasing the surface area: the surface tension. Since you'd apply a force parallel to the surface to extend the area, as shown below, the corresponding restoring force is also parallel to the surface.
Chemomechanics
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Its a little like the definition of friction. The force components parallel to the surface are called the surface tension. The downward component is what works against evaporation.
R.W. Bird
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