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The span of two arbitrary vectors $\vec{v}$ and $\vec{w}$ that do not lie on the same line is the entire 2D plane. This is achieved by taking all possible linear combinations $a\vec{v} + b\vec{w}$ where scalars $a$ and $b$ vary continuously across all real numbers.

Conditions: Two vectors $\vec{v}$ and $\vec{w}$ are nonzero; Vectors $\vec{v}$ and $\vec{w}$ are non-collinear (point in different directions)

The span of two arbitrary vectors $\vec{v}$ and $\vec{w}$ that do not lie on the same line is the entire 2D plane. This is achieved by taking all possible linear combinations $a\vec{v} + b\vec{w}$ where scalars $a$ and $b$ vary continuously across all real numbers.

Conditions: Two vectors $\vec{v}$ and $\vec{w}$ are nonzero; Vectors $\vec{v}$ and $\vec{w}$ are non-collinear (point in different directions)