Vector Magnitude Proof

Want to find the magnitude of a vector?

You quite simply have to know that:

{ \left| \underline { v }  \right|  }^{ 2 }={ \underline { v }  }^{ 2 }

And that if:

\underline { v } =\left( \begin{matrix} x \\ y \\ z \end{matrix} \right) ,\quad { \underline { v }  }^{ 2 }={ x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }

So:

If\quad { \underline { v }  }^{ 2 }={ x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 },\\ \\ \therefore \quad { \left| \underline { v }  \right|  }^{ 2 }={ x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }\\ \\ \therefore \quad \left| \underline { v }  \right| =\sqrt { { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } } \\

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