Question

given vectors u = ⟨-1,3⟩ and v = ⟨-3,3⟩, find the sum u + v and write the result in component form. click and drag either vector to add graphically.

Explanation:

Step1: Recall vector - addition formula

For two - dimensional vectors $\mathbf{u}=\langle u_1,u_2
angle$ and $\mathbf{v}=\langle v_1,v_2
angle$, the sum $\mathbf{u}+\mathbf{v}=\langle u_1 + v_1,u_2 + v_2
angle$.

Step2: Identify the components of the given vectors

Given $\mathbf{u}=\langle - 1,3
angle$ and $\mathbf{v}=\langle - 3,3
angle$, where $u_1=-1$, $u_2 = 3$, $v_1=-3$, and $v_2 = 3$.

Step3: Calculate the sum of the vectors

$\mathbf{u}+\mathbf{v}=\langle - 1+( - 3),3 + 3
angle=\langle-1 - 3,6
angle=\langle-4,6
angle$.

Answer:

$\langle-4,6
angle$