The sum and difference with algebraic vector notation

$$\overrightarrow{AB}$$ - 

A vector starting from $$A$$ and ending at $$B$$

$$AB$$ - 

A line segment with points $$A$$ and $$B$$ at each end

$$\overrightarrow{BA}$$ - 

A vector starting from $$B$$ and ending at $$A$$

$$(a,b)$$ - 

A point with $$x$$-coordinate of $$a$$ and $$y$$-coordinate of $$b$$

$$(b,a)$$ - 

A point with $$x$$-coordinate of $$b$$ and $$y$$-coordinate of $$a$$

$${8 \choose -2} + {4 \choose 9}$$ - 

$${12 \choose 7}$$

$$3{5 \choose 6}$$ - 

$${15 \choose 18}$$

$${4\choose 9} + {-2 \choose -4}$$ - 

$${2 \choose 5}$$

$${-4\choose 10} - {9 \choose 9}$$ - 

$${-13\choose 1}$$

$$2{2.5 \choose -3.5}$$ - 

$${5 \choose -7}$$

$$x = 5$$ - 

$${13 \choose -2} + {12 \choose 7} = {25 \choose x} $$

$$x=-7$$ - 

$${12 \choose x} + {-7 \choose -7} = {5 \choose -14} $$

$$x=2$$ - 

$$4{x \choose 8} = {8 \choose 16} $$

$$x=8$$ - 

$${3\choose 4} + {x \choose -4} = {11 \choose 0} $$

$$\mathbf{a}$$ - 

$${6 \choose 0}$$

$$\mathbf{b}$$ - 

$${-2 \choose -2}$$

$$\mathbf{c}$$ - 

$${4 \choose -2}$$

$$\mathbf{d}$$ - 

$${-2 \choose -3}$$

$$\mathbf{e}$$ - 

$${-8\choose -2}$$

$$\mathbf{f}$$ - 

$${-6\choose 1}$$

$$\overrightarrow{AB}$$ - 

$${2\choose 2}$$

$$\overrightarrow{BC}$$ - 

$${2\choose 3}$$

$$\overrightarrow{BD}$$ - 

$${8\choose 2}$$

$$\overrightarrow{EA}$$ - 

$${-8\choose 0}$$

$$\overrightarrow{EB}$$ - 

$${-4\choose 2}$$

$$3{4 \choose -7} + 2{2 \choose 4}$$ - 

$${16 \choose -13} $$

$$2{4 \choose -7} + 5{-2 \choose 4}$$ - 

$${-2 \choose 6} $$

$$4{2 \choose 5}$$ - 

$${8 \choose 20} $$

$$3{4 \choose -2} + 3{-2 \choose 5} $$ - 

$${6 \choose 9} $$

$$\overrightarrow{OC}$$ - 

$$3\mathbf{a} -\mathbf{b} + 3\mathbf{d}$$

$$\overrightarrow{BD}$$ - 

$$\mathbf{a} -4\mathbf{b} + 3\mathbf{d}$$

$$\overrightarrow{AC}$$ - 

$$\mathbf{a} -3\mathbf{b} + 3\mathbf{d}$$

$$\overrightarrow{CE}$$ - 

$$-\mathbf{a}-4\mathbf{b} - 2\mathbf{d}$$