Question

let \\( \mathbf{u} = 6\mathbf{i} - 4\mathbf{j} \\) and \\( \mathbf{v} = -7\mathbf{i} + 8\mathbf{j} \\). find the vector \\( \mathbf{u} + \mathbf{v} \\).\\( \mathbf{u} + \mathbf{v} = \square \\) (simplify your answer. type your answer in terms of \\( \mathbf{i} \\) and \\( \mathbf{j} \\).)

Explanation:

Step1: Add i-components

$(6 + (-7))\mathbf{i} = -1\mathbf{i}$

Step2: Add j-components

$(-4 + 8)\mathbf{j} = 4\mathbf{j}$

Step3: Combine the results

$\mathbf{u}+\mathbf{v} = (-1\mathbf{i}) + (4\mathbf{j})$

Answer:

$-\mathbf{i} + 4\mathbf{j}$