Question

Find the sum of the following vectors:
$\overrightarrow{a}=\hat{i}-3\hat{k},.\overrightarrow{b}=2\hat{j}-\hat{k},\overrightarrow{c}=2\hat{i}-3\hat{j}+2\hat{k}$

Answer 1

Add the vectors

$\overrightarrow{a}=\hat{i}-3\hat{k}$, $\overrightarrow{b}=2\hat{j}-\hat{k}$ and $\overrightarrow{c}=2\hat{i}-3\hat{j}+2\hat{k}$

by writing them in the component form that is

$\overrightarrow{a}=⟨1,0,-3⟩$, $\overrightarrow{b}=⟨0,2,-1⟩$ and $\overrightarrow{c}=⟨2,-3,2⟩$

The sum of the vectors can be computed as follows:

$\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=(1+0+2,0+2-3,-3-1+2)$

$=⟨3,-1,-2⟩$

Hence the sum of the vectors is $⟨3,-1,-2⟩$.