91Ó°ÊÓ

Find the component form and magnitude of the vector v. $$\begin{array}{cc}\text{Initial Point} && \text{Terminal Point} \\ (1,3) && (-8,-9) \end{array}$$

Use the vectors \(\mathbf{u}=\langle\mathbf{3}, \mathbf{3}\rangle, \mathbf{v}=\langle-\mathbf{4}, \mathbf{2}\rangle,\) and \(\mathbf{w}=\langle 3,-1\rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. $$2-\|\mathbf{u}\|$$

Find the component form and magnitude of the vector v. $$\begin{array}{cc}\text{Initial Point} && \text{Terminal Point} \\ (1,11) && (9,3) \end{array}$$

Use the Law of cosines to solve the triangle. Round your answers to two decimal places. $$C=15^{\circ} 15^{\prime}, \quad a=7.45, \quad b=2.15$$

Use the vectors \(\mathbf{u}=\langle\mathbf{3}, \mathbf{3}\rangle, \mathbf{v}=\langle-\mathbf{4}, \mathbf{2}\rangle,\) and \(\mathbf{w}=\langle 3,-1\rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. $$(\mathbf{u} \cdot \mathbf{v})-(\mathbf{u} \cdot \mathbf{w})$$

Find the component form and magnitude of the vector v. $$\begin{array}{cc}\text{Initial Point} && \text{Terminal Point} \\ (-1,5) && (15,12) \end{array}$$

Trigonometric Form of a Complex Number Represent the complex number graphically. Then write the trigonometric form of the number. $$2 \sqrt{2}-i$$

Use the Law of cosines to solve the triangle. Round your answers to two decimal places. $$C=43^{\circ}, \quad a=\frac{4}{9}, \quad b=\frac{7}{9}$$

Use the Law of sines to solve the triangle. Round your answers to two decimal places. \(A=110^{\circ} 15^{\prime}, \quad a=48, \quad b=16\)

Use the vectors \(\mathbf{u}=\langle\mathbf{3}, \mathbf{3}\rangle, \mathbf{v}=\langle-\mathbf{4}, \mathbf{2}\rangle,\) and \(\mathbf{w}=\langle 3,-1\rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. $$(\mathbf{v} \cdot \mathbf{u})-(\mathbf{w} \cdot \mathbf{v})$$