Question

let u = 7i - 8j, and w = -i - 5j. find ||w - u||. ||w - u|| = \square (type an exact answer, using radicals as needed.)

Explanation:

Step1: Compute $\mathbf{w}-\mathbf{u}$

Subtract components of $\mathbf{u}$ from $\mathbf{w}$:
$$\mathbf{w}-\mathbf{u} = (-1 - 7)\mathbf{i} + (-5 - (-8))\mathbf{j} = -8\mathbf{i} + 3\mathbf{j}$$

Step2: Calculate the magnitude

Use magnitude formula $\|\mathbf{v}\|=\sqrt{a^2+b^2}$ for $\mathbf{v}=a\mathbf{i}+b\mathbf{j}$:
$$\|\mathbf{w}-\mathbf{u}\| = \sqrt{(-8)^2 + 3^2} = \sqrt{64 + 9} = \sqrt{73}$$

Answer:

$\sqrt{73}$