Question

Sejam Vectores U=(2;3) e V=(-2;1)
Como determinar a) U+V ilustrar geometricamente
B) 3U-4V
C) || U+V||

Answer 1

a)

$U+V~=~(2~,~3)~+~(-2~,~1)\\\\\\U+V~=~(2+(-2)~,~3+1)\\\\\\\boxed{U+V~=~(0~,~4)}$

b)

$3U-4V~=~3\,.\,(2~,~3)~-~4\,.\,(-2~,~1)\\\\\\3U-4V~=~(3\,.\,2~,~3\,.\,3)~-~(4\,\.,(-2)~,~4\,.\,1)\\\\\\3U-4V~=~(6~,~9)~-~(-8~,~4)\\\\\\3U-4V~=~(6-(-8)~,~9-4)\\\\\\\boxed{3U-4V~=~(14~,~5)}$

c)

$\left\|U+V\right\|~=~\sqrt{(0)^2+(4)^2}\\\\\\\left\|U+V\right\|~=~\sqrt{0+16}\\\\\\\left\|U+V\right\|~=~\sqrt{16}\\\\\\\boxed{\left\|U+V\right\|~=~4}$