$\vec{a} = \hat{i} - 2\hat{j} + 4\hat{k}$, $\vec{b} = 3\hat{i} + \hat{j} - \hat{k}$ and $\vec{c} = -2\hat{i} - 2\hat{j} + 3\hat{k}$. What is $\lvert \vec{a} + \vec{b} + \vec{c} \rvert$?

Explanation

1. 01

   $\vec{a} + \vec{b} + \vec{c} = (1 + 3 - 2)\hat{i} + (-2 + 1 - 2)\hat{j} + (4 - 1 + 3)\hat{k} = 2\hat{i} - 3\hat{j} + 6\hat{k}$.

2. 02

   $\lvert \vec{a} + \vec{b} + \vec{c} \rvert = \sqrt{4 + 9 + 36} = 7$.