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}`