If $\overrightarrow{A} = 3\widehat{i} + 2\widehat{j}$ and $\overrightarrow{B} = \widehat{i} + \widehat{j} - 2\widehat{k}$,find their sum using the algebraic method.

(N/A) To find the sum of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$,we add their corresponding components:
$\overrightarrow{A} + \overrightarrow{B} = (3\widehat{i} + 2\widehat{j}) + (1\widehat{i} + 1\widehat{j} - 2\widehat{k})$
Grouping the components of $\widehat{i}$,$\widehat{j}$,and $\widehat{k}$:
$= (3 + 1)\widehat{i} + (2 + 1)\widehat{j} + (0 - 2)\widehat{k}$
$= 4\widehat{i} + 3\widehat{j} - 2\widehat{k}$