Given the vector [tex]\vec{r}(a,b,c,d)[/tex].
Now taking the vertices of parallelogram asA [tex]\vec{a},B\vec{b},C\vec{c},D\vec{d}[/tex].
As we know to find the edges of parallelogram ABCD,we proceed as follows
[tex]\vec{AB}[/tex]= Position vector of B - Position vector of A
[tex]\vec{b}-\vec{a}[/tex]
[tex]\vec{BC}[/tex]= Position vector of C - Position vector of B
=[tex]\vec{c}-\vec{b}[/tex]
[tex]\vec{CD}[/tex]= Position vector of D - Position vector of C
= [tex]\vec{d}-\vec{c}[/tex]
[tex]\vec{DA}[/tex]= Position vector of A - Position vector of D
=[tex]\vec{a}-\vec{d}[/tex]
So, [tex]\vec{b}-\vec{a},\vec{c}-\vec{b},\vec{d}-\vec{c},\vec{a}-\vec{d}[/tex] are edges of parallelogram.
