Question

Describe two vectors a and b such that a overscript right-arrow endscripts plus b overscript right-arrow endscripts equals c overscript right-arrow endscripts and a plus b equals c

Answer 1

Define the two vectors as
$\vec{a} = a_{x} \hat{i} + a_{y}\hat{j} + a_{z}\hat{k} \\ \vec{b}=b_{x}\hat{i}+b_{y}\hat{j}+b_{z}\hat{k}$

Then if vector c is defined by
$\vec{c}=\vec{a}+\vec{b}$
then
$\vec{c}=(a_{x}+b_{x})\hat{i} + (a_{y}+b_{y})\hat{j} + (a_{z}+b_{z})\hat{k}$

Example:
If
$\vec{a}=3\hat{i}-7\hat{j} \\ \vec{b}=-2\hat{i}+5\hat{k}$
then
$\vec{c}=(3-2)\hat{i}+(-7+0)\hat{j}+(0+5)\hat{k} \\ \vec{c}=\hat{i}-7\hat{j}+5\hat{k}$