Question

Given the vectors u=6i-4j and v=-i+2j, find -2u and u+v Write your answers in the form ai +bj-2u=U+v=

Answer 1

Recall that:

`\begin{gathered} \text{For all a,b,c,d,e real numbers:} \\ (ai+bj)+(ci+dj)=(a+c)i+(b+d)j, \\ e(ai+bj)=(ea)i+(eb)j\text{.} \end{gathered}`

Therefore:

`\begin{gathered} -2u=-2(6i-4j)=(-2\cdot6)i+(-2(-4))j=-12i+8j. \\ u+v=(6i-4j)+(-i+2j)=(6-1)i+(-4+2)j=5i-2j\text{.} \end{gathered}`

Answer:

`\begin{gathered} -2u=-12i+8j. \\ u+v=5i-2j\text{.} \end{gathered}`