Question

let \\( \mathbf{v} = -6\mathbf{i} - 8\mathbf{j} \\). find the vector \\( -5\mathbf{v} \\). \\( -5\mathbf{v} = \square \\) (simplify your answer. type your answer in terms of \\( \mathbf{i} \\) and \\( \mathbf{j} \\).)

Explanation:

Step1: Multiply scalar by vector components

$-5\mathbf{v} = -5(-6\mathbf{i} -8\mathbf{j})$

Step2: Distribute scalar to each term

$= (-5 \times -6)\mathbf{i} + (-5 \times -8)\mathbf{j}$

Step3: Calculate scalar products

$= 30\mathbf{i} + 40\mathbf{j}$

Answer:

$30\mathbf{i} + 40\mathbf{j}$