MathAlgebraLinear algebraVectors and vector spaces

Vector norm and distance between vectors

Proper norm

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Which of the following must be true for a valid norm:

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\|\overrightarrow{u}\| = 1 \Leftrightarrow \overrightarrow{u} = \overrightarrow{0}

\|\overrightarrow{u}+\overrightarrow{v}\| \leq \|\overrightarrow{u}\|+\|\overrightarrow{v}\|

\|\overrightarrow{u}\| = 0 \Leftrightarrow \overrightarrow{u} = \overrightarrow{0}

\|\overrightarrow{u}+\overrightarrow{v}\| = \|\overrightarrow{u}\|+\|\overrightarrow{v}\|

\|k \cdot \overrightarrow{u}\| = |k| \cdot \|\overrightarrow{u}\|

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