91Ó°ÊÓ

Find \(\mathbf{u} \cdot \mathbf{v}.\) $$\begin{aligned}&\mathbf{u}=\langle-4,1\rangle\\\&\mathbf{v}=\langle 2,-3\rangle\end{aligned}$$

The vector sum \(v_{1} \mathbf{i}+v_{2} \mathbf{j}\) is called a _____ _____ of the vectors \(\mathbf{i}\) and \(\mathbf{j},\) and the scalars \(v_{1}\) and \(v_{2}\) are called the _____ and _____ components of \(\mathbf{v},\) respectively.

Find \(\mathbf{u} \cdot \mathbf{v}.\) $$\begin{aligned}&\mathbf{u}=\langle-2,5\rangle\\\&\mathbf{v}=\langle-1,-8\rangle\end{aligned}$$

Trigonometric Form of a Complex Number Represent the complex number graphically. Then write the trigonometric form of the number. $$1+i$$

Use the Law of sines to solve the triangle. Round your answers to two decimal places. \(A=83^{\circ} 20^{\prime}, \quad C=54.6^{\circ}, \quad c=18.1\)

Find \(\mathbf{u} \cdot \mathbf{v}.\) $$\begin{aligned}&\mathbf{u}=4 \mathbf{i}-2 \mathbf{j}\\\&\mathbf{v}=\mathbf{i}-\mathbf{j}\end{aligned}$$

Find \(\mathbf{u} \cdot \mathbf{v}.\) $$\begin{aligned}&\mathbf{u}=3 \mathbf{i}+4 \mathbf{j}\\\&\mathbf{v}=7 \mathbf{i}-2 \mathbf{j}\end{aligned}$$

Trigonometric Form of a Complex Number Represent the complex number graphically. Then write the trigonometric form of the number. $$5-5 i i$$

Use the Law of sines to solve the triangle. Round your answers to two decimal places. \(A=5^{\circ} 40^{\prime}, \quad B=8^{\circ} 15^{\prime}, \quad b=4.8\)

Find \(\mathbf{u} \cdot \mathbf{v}.\) $$\begin{aligned}&\mathbf{u}=3 \mathbf{i}+2 \mathbf{j}\\\&\mathbf{v}=-2 \mathbf{i}-3 \mathbf{j}\end{aligned}$$