Let [math]a^{\rightarrow}=\left(a_1,a_2\right)[/math] and [math]b^{\rightarrow}=\left(b_1,b_2\right)[/math] be any two vectors. Then the sum of the vectors [math]a^{\rightarrow}[/math] and[math]b^{\rightarrow}[/math] and, denoted by [math]a^{\rightarrow}[/math]+[math]b^{\rightarrow}[/math]= [math]\left(a_1,a_2\right)[/math]+[math]\left(b_1,b_2\right)[/math]= [math]\left(a_1_{ }+b_1,a_2+b_2\right)[/math]. Example: (2,3) + (4,8) = (2+4,3+8) = (6,11)

Let [math]a^{\rightarrow}=\left(a_1,a_2\right)[/math]and [math]b^{\rightarrow}=\left(b_1,b_2\right)[/math] be any two vectors. Then the difference of the vectors [math]a^{\rightarrow}[/math] and [math]b^{\rightarrow}[/math], denoted by [math]a^{\rightarrow}-b^{\rightarrow}[/math], is defined as [math]a^{\rightarrow}-b^{\rightarrow}=\left(a_1,a_2\right)-\left(b_1,b_2\right)[/math] . Example: Let [math]a^{\rightarrow}=\left(5,9\right)[/math] and [math]b^{\rightarrow}=\left(6,10\right)[/math] be the two vectors. Then their difference is [math]a^{\rightarrow}-b^{\rightarrow}[/math] [math]\left(5,9\right)-\left(6,10\right)=\left(-1,-1\right)[/math].

[b]Statement: [/b] If any two vectors acting at a point can be represented by the two sides of a triangle then their sum is represented by the third side of the triangle taken in reverse order. It is shown in the following figure:

[b]Statement:[/b] The sum of any two vectors acting at a point is represented geometrically by the diagonal of a parallelogram which is made by the magnitudes of the vectors as its adjacent sides and the diagonal representing the sum passes through that point at which the vectors are acting. This is the famous parallelogram law of addition of vectors. This is illustrated in the succeeding figure.