## Friday, 8 August 2014

### CHAPTER 3-Subtraction of Vectors

Consider two vectors $\vec a$ and $\vec b$; we wish to find $\vec c$ such that
 $\vec c = \vec a - \vec b$
We can slightly modify this relation and write it as
 $\vec c = \vec a + \left( { - \vec b} \right)$
and thus subtraction can be treated as addition. To do this, we first reverse the vector $\vec b$ to obtain $- \,\vec b$ and then use the triangle / parallelogram law of addition to add the vector $\vec a$ and $( - \vec b)$:
Joining the tip of $\vec b$ to the tip of $\vec a$ (if $\vec a$ and $\vec b$ are co-initial) also gives us $\vec a - \vec b.$
Note that from the triangle law, it follows that for three vectors $\vec a,\vec b$ and $\vec c$representing the sides of a triangle as shown,
We must have
 $\vec a + \vec b + \vec c = \vec 0$
In fact, for the vectors ${\vec a_i},\,\,i = 1,2\ldots n,$ representing the sides of an $n$-sided polygon as shown,
we must have
 ${\vec a_1} + {\vec a_2} + \ldots+ {\vec a_n} = \vec 0$
since the net effect of all vectors is to bring us back from where we started, and thus our net displacement is the zero vector.