Question

question: given vectors u = ⟨ - 5,2⟩ and v = ⟨2,8⟩, 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 components of given vectors

Given $\mathbf{u}=\langle - 5,2
angle$ and $\mathbf{v}=\langle2,8
angle$, where $u_1=-5$, $u_2 = 2$, $v_1 = 2$, and $v_2 = 8$.

Step3: Calculate the sum of the vectors

$\mathbf{u}+\mathbf{v}=\langle-5 + 2,2 + 8
angle=\langle-3,10
angle$.

Answer:

$\langle-3,10
angle$