Find the sum of the vectors

Question:

Find the sum of the vectors $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}, \vec{b}=-2 \hat{i}+4 \hat{j}+5 \hat{k}$ and $\vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}$.

Solution:

The given vectors are $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}, \vec{b}=-2 \hat{i}+4 \hat{j}+5 \hat{k}$ and $\vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}$.

$\therefore \vec{a}+\vec{b}+\vec{c}=(1-2+1) \hat{i}+(-2+4-6) \hat{j}+(1+5-7) \hat{k}$

$=0 \cdot \hat{i}-4 \hat{j}-1 \cdot \hat{k}$

$=-4 \hat{j}-\hat{k}$