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The length of a vector is also sometimes called the magnitude or the norm of a vector.
The length or magnitude or norm of the vector \(\vec{a}\) is denoted by \(\|\vec{a}\|\) or, less commonly, \(\lvert\vec{a}\rvert\)
The length of a \(n\)-dimensional vector \(\vec{V}\) is a scalar given by the formula:
\[\|\vec{V}\| = \sqrt{\sum_{i=1}^{n}{V_i^2}} \]
The length of a \(two\)-dimensional vector \(\vec{a}\) is a scalar given by the formula:
\(\|\vec{a}\| = \sqrt{a_x^2 + a_y^2}\)
| x | y | |
|---|---|---|
| \(\vec{a}\) | ||
| \(\|\vec{a}\| = \sqrt{a_x^2 + a_y^2}\) | ||