Question

given \\( \mathbf{u} = \langle 4, -4 \
angle \\) and \\( \mathbf{v} = \langle -3, 5 \
angle \\), then \\( \mathbf{u} \cdot \mathbf{v} = \\) \\( \boxed{} \\) question help: \\( \boldsymbol{\text{message instructor}} \\) \\( \boldsymbol{\text{submit and end}} \\)

Explanation:

Step1: Recall Dot Product Formula

For vectors \(\mathbf{u} = \langle u_1, u_2
angle\) and \(\mathbf{v} = \langle v_1, v_2
angle\), the dot product \(\mathbf{u} \cdot \mathbf{v}=u_1v_1 + u_2v_2\).

Step2: Identify Components

Here, \(u_1 = 4\), \(u_2=- 4\), \(v_1=-3\), \(v_2 = 5\).

Step3: Compute Dot Product

Substitute into the formula: \(\mathbf{u}\cdot\mathbf{v}=(4)(-3)+(-4)(5)\)
Calculate each term: \(4\times(-3)=-12\), \(-4\times5 = - 20\)
Sum the terms: \(-12+(-20)=-32\)

Answer:

\(-32\)