$\vec{a}$, $\vec{b}$ and $\vec{c}$ are mutually perpendicular, with $\lvert \vec{a} \rvert = 2$, $\lvert \vec{b} \rvert = 3$ and $\lvert \vec{c} \rvert = 6$. What is $\lvert \vec{a} + \vec{b} + \vec{c} \rvert$?

Explanation

1. 01

   $\lvert \vec{a} + \vec{b} + \vec{c} \rvert^{2} = \lvert \vec{a} \rvert^{2} + \lvert \vec{b} \rvert^{2} + \lvert \vec{c} \rvert^{2} + 2(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a})$.

2. 02

   Every scalar product is 0, so it is $4 + 9 + 36 = 49$, and $\lvert \vec{a} + \vec{b} + \vec{c} \rvert = 7$.