Question

1. show that $vec{u}=(3,1)$ added to $vec{v}=(-1,-1)$ is $vec{k}=(2,0)$. label your vectors

Explanation:

Step1: Recall vector - addition formula

For two - dimensional vectors $\vec{u}=(u_1,u_2)$ and $\vec{v}=(v_1,v_2)$, the sum $\vec{u}+\vec{v}=(u_1 + v_1,u_2 + v_2)$.

Step2: Identify components of given vectors

Here, $\vec{u}=(3,1)$ where $u_1 = 3$ and $u_2 = 1$, and $\vec{v}=(-1,-1)$ where $v_1=-1$ and $v_2=-1$.

Step3: Calculate the sum

$\vec{u}+\vec{v}=(u_1 + v_1,u_2 + v_2)=(3+( - 1),1+( - 1))$.
$3+( - 1)=3 - 1 = 2$ and $1+( - 1)=1 - 1 = 0$. So, $\vec{u}+\vec{v}=(2,0)$.

Answer:

The sum of $\vec{u}=(3,1)$ and $\vec{v}=(-1,-1)$ is $(2,0)$ as shown by the vector - addition formula $\vec{u}+\vec{v}=(u_1 + v_1,u_2 + v_2)$.