Why is surface tension represented as forces at triple line? And why are they balanced horizontally only? I thought that direction of surface tension is along the tangent to the surface which is best explained by this diagram which I found this diagram in Wikipedia

But recently I saw in a book the diagram below

Where

I know that their direction are along the tangent to interface .... but I didn't understand why $S_{sl}$ is towards right and $S_{sa}$ towards left ??
Also, they give the following equation:

I understand that they took equilibrium at point of contact along horizontal direction.
What if we consider balance along vertical direction?
I got $S_{la} \sin θ$ upwards. What are other vertical forces ? Are they weight, normal reaction ??
 A: The interfacial tension is along all interfaces, so along liquid-air interface (your Wikipedia diagram), but also solid-air and solid-liquid, thus along the $z=0$ line in the diagram of a liquid droplet.
At the triple point, the boundary condition for these tensions are forces (just as the tension of a spring is equal to the force it exerts on surrounding at the point where it is clamped), and these forces are tangential to the interface they belong to, pointing towards the interface is tension is positive, hence the 3 arrows there.
In the appropriate plane perpendicular to triple line, these forces are 2D vectors in $(x,z)$, so you can solve the balance along $x$ and along $z$. The $x$ balance is the one that will give you information, e.g allow to solve for $\theta$, and that's why people usually only focus on this one.
There is also a balance in $z$, of course: you have a resisting force from the substrate equal and opposite to the $z$ component of the line tension. If substrate is deformable, you get a little ridge forming there :

(Taken from DOI: 10.1039/C3SM51184G)
But because, for an undeformable substrate, it is a reaction force that will adjust to the pull of liquid-air interface, it does not give you any information in that case.
It is the principle behind what some researchers have called capillary origami:

See also the video and paper there
Note that globally also, force balance is enforced as the pressure force exerted downwards by the drop on the substrate all along the $a$ region in diagram exactly balances this upward line force.
