consider a matrix A = USV’
A = [1 2;3 4;5 6]
the matrix U is
[-0.23 0.97;-0.97 -0.23;0.06 -0.01]
choose the first column of A as the individual data vector a1 = (1,3,5)
the inner product of u1 is u1*a1=-0.23*1+-0.97*3+0.06*5=-3.11
so the inner product is negative, choose flip the sign of u1 = -u1 = (0.23, 0.97,-0.06)

So Why does multiplying a column of data give direction of singular vector? What is the meaning of this process?

I was try to using PCA on my image, find out why the direction is always choose the thin end