Question

let \\( \mathbf{u} = 5\mathbf{i} - 3\mathbf{j} \\), and \\( \mathbf{v} = -9\mathbf{i} + 3\mathbf{j} \\). find \\( \mathbf{v} - \mathbf{u} \\).\\( \mathbf{v} - \mathbf{u} = \square \\) (type your answer in terms of \\( \mathbf{i} \\) and \\( \mathbf{j} \\).)

Explanation:

Step1: Substitute vector expressions

$\mathbf{v}-\mathbf{u}=(-9\mathbf{i}+3\mathbf{j})-(5\mathbf{i}-3\mathbf{j})$

Step2: Distribute the negative sign

$\mathbf{v}-\mathbf{u}=-9\mathbf{i}+3\mathbf{j}-5\mathbf{i}+3\mathbf{j}$

Step3: Combine like terms

$\mathbf{v}-\mathbf{u}=(-9-5)\mathbf{i}+(3+3)\mathbf{j}$

Step4: Calculate coefficients

$\mathbf{v}-\mathbf{u}=-14\mathbf{i}+6\mathbf{j}$

Answer:

$-14\mathbf{i}+6\mathbf{j}$