$I.$ The zero vector is linearly dependent.
$II.$ Any set containing the zero vector must be linearly dependent.
I only apprehend the truths of I and II above from the definition of linear independence :
http://math.berkeley.edu/~mjv/lindep0.pdf
www.math.ku.edu/~lerner/LAnotes/Chapter11.pdf
Howbeit, I'm not perceiving the intuition behind $I$ and $II$. For instance, in this first set of 2 pictures, the $\color{red}{u}$ $\in \mathbb{R}^2$ originates from $\color{#1E90FF}{0},$ and thus makes contact/"intersects" with $\color{#1E90FF}{0}$. So how and why isn't it dependent (on $\color{#1E90FF}{0})$?
Beyond geometric intuition(s) and this interpretation, what are other intuitions for $I$ and $II$?
This page precedes basis, dimension, Orthogonality, Determinants, Eigenvalues and eigenvectors, and linear transformations, so please omit these concepts in responses.