Question

find the magnitude of u using the dot product. write the result in radical form or decimal form, rounded to the nearest hundredth.
u = \langle - 5, - 8 \
angle

Explanation:

Step1: Recall the formula for the magnitude using the dot product

The magnitude of a vector \(\mathbf{u}=\langle a,b
angle\) is \(|\mathbf{u}|=\sqrt{\mathbf{u}\cdot\mathbf{u}}\), and if \(\mathbf{u}=\langle a,b
angle\) and \(\mathbf{v}=\langle c,d
angle\), then \(\mathbf{u}\cdot\mathbf{v}=ac + bd\). For \(\mathbf{u}=\langle - 5,-8
angle\), \(\mathbf{u}\cdot\mathbf{u}=(-5)\times(-5)+(-8)\times(-8)\).

Step2: Calculate the dot - product

$$
LATEXBLOCK0
$$

Step3: Calculate the magnitude

Since \(|\mathbf{u}|=\sqrt{\mathbf{u}\cdot\mathbf{u}}\), and \(\mathbf{u}\cdot\mathbf{u} = 89\), then \(|\mathbf{u}|=\sqrt{89}\approx9.43\)

Answer:

The magnitude of \(\mathbf{u}\) is \(\sqrt{89}\approx9.43\)