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It's quite confusing.Principle of superposition states that the amplitude of two superposing wave eqauls their indivisual amplitude vector sum.But what about direction.Souldnt't wave direction of propagation should also add up and the most confusing part is that the wave continue traveling unchanged after superposition why is it show?Why the change is not permanent?

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The direction does not change due to the same superposition principle.

Let's look at two waves, red and blue, at the diagram below.

enter image description here

The waves intersect and interfere with each other in the area A. The direction of the red wave at point B, beyond the intersection and interference with the blue wave ("after superposition"), should not be affected by this interference, because, according to the superposition principle, the field at B is the sum of the fields produced by the red and blue waves at point B, when they act alone, but the effect of the blue wave, acting along at point B, is obviously zero.

Therefore, the field at B is affected by the red blue only and, therefore, the direction of the red wave at B should be the same regardless of the presence of the blue wave and the interference between the two waves at A.

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