Calculate the scalar product of the following vectors.
Given three vectors $a=\{3,-1\},b=\{1,-2\},andc=\{-1,7\}.$ Determine the resolution of the vector $p=a+b+c$ into components with respect to the vectors a and b.

We are required to find p in terms of a and b let $p=ax+by$

$a+b+c=ax+by$

$(3,-1)+(1,-2)+(-1,7)=x(3,-1)+y(1,-2)$

$(3,4)=(3x+y,-x-2y)$

$3x+y=\mathrm{3............}\left(1\right)$

$-x-2y=\mathrm{4..........}\left(2\right)$

Equation $2\times \left(1\right)+\left(2\right)$

$5x=10\Rightarrow x=2$

by substituting x=2 in (1), we get

$y=-3$

$p=2a-3b$