Question

question given vectors u = (-1, -5) and v = (-7, 3), find the sum u + v and write the result in component form.

Explanation:

Step1: Recall vector - addition rule

To add two vectors $\mathbf{u}=(u_1,u_2)$ and $\mathbf{v}=(v_1,v_2)$, we use the formula $\mathbf{u}+\mathbf{v}=(u_1 + v_1,u_2 + v_2)$. Here, $u_1=-1$, $u_2=-5$, $v_1=-7$, and $v_2 = 3$.

Step2: Add the first components

Add the first - components of $\mathbf{u}$ and $\mathbf{v}$: $u_1 + v_1=-1+( - 7)=-1 - 7=-8$.

Step3: Add the second components

Add the second - components of $\mathbf{u}$ and $\mathbf{v}$: $u_2 + v_2=-5 + 3=-2$.

Answer:

$\langle - 8,-2
angle$