Q.Is surface tension a vector?

Concept: Nature of surface tension as a physical quantity.

Surface tension $T$ is defined as the force per unit length acting along the boundary of a liquid surface:

While the force due to surface tension acts tangentially along the liquid surface and has direction, surface tension itself is the magnitude of this force per unit length. It characterizes the intensity of the molecular cohesive forces at the surface, independent of any particular direction. …

Why surface tension is scalar

Surface tension $\gamma$ measures the energy cost of creating new surface area, or equivalently the force exerted per unit length along any line drawn on a liquid surface. Its defining equation is

where $F$ is the force acting perpendicular to a line of length $L$ on the surface. At first glance this looks directional: the force certainly has a direction. But the key is that surface tension itself is the magnitude of force per unit length, not the force vector.

Think of it this way: if you draw a line anywhere on a soap film, the film pulls perpendicular to that line with the same intensity $\gamma$ regardless of which direction you drew the line. The direction of the resulting force depends on the orientation of the line you chose, but $\gamma$ itself—the "tightness" or "tension" of the surface—is the same everywhere and has no preferred direction built into it.

Why the confusion arises

1. Surface tension produces forces that are vectors. When you calculate the force on a wire frame in contact with a liquid surface, you use $\vec{F} = \gamma L \,\hat{n}$, where $\hat{n}$ is perpendicular to the contact line. That force is a vector, but $\gamma$ is the scalar coefficient.

2. It acts along a line. This makes it feel one-dimensional or directional. But "acting along a line" means it exerts force perpendicular to any line element; the scalar $\gamma$ quantifies the strength, while geometry determines the direction. …

gamma=F/L defined per unit length along any line on the surface. Direction of the resulting force comes from the line's own geometry (perpendicular to it), not from gamma itsel …