I am learning R and have a question about general mathematical terminology

This three dimensional array has

a <- array(rnorm(2*2*10), c(2,2,10))

- 2 rows

- 2 columns

- 10 units in a third dimension (layers?)

‘Layer’ sounds to me like a good term for the dimension along the z-axis. Does anyone else know of a more widely used term for it?

Thinking along the lines of orthogonal components in principal components analysis (PCA), there may be a whole set of terms. Does one exist? Is it or would one be helpful to improve communication between researchers? I have heard 1st, 2nd, and 3rd component in the context of PCA, but don’t know if they translate well to other types of multi-dimensional calculations.