91Ó°ÊÓ

In Exercises \(39-46,\) find the unit vector that has the same direction as the vector \(\mathbf{v}\). $$\mathbf{v}=-5 \mathbf{j}$$

A plane leaves airport \(A\) and travels 580 miles to airport \(B\) on a bearing of \(\mathrm{N} 34^{\circ} \mathrm{E}\). The plane later leaves airport \(\mathrm{B}\) and travels to airport \(\mathrm{C} 400\) miles away on a bearing of \(\mathrm{S} 74^{\circ} \mathrm{E}\). Find the distance from airport \(A\) to airport \(C\) to the nearest tenth of a mile.

Polar coordinates of a point are given. Find the rectangular coordinates of each point. $$(8.3,4.6)$$

Test for symmetry and then graph each polar equation. $$r=\frac{2}{1-\cos \theta}$$

The rectangular coordinates of a point are given. Find polar coordinates of each point. Express \(\theta\) in radians. $$(-2,2)$$

Let $$\mathbf{u}=-\mathbf{i}+\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \text { and } \quad \mathbf{w}=-5 \mathbf{j}$$ Find each specified scalar or vector. $$\operatorname{proj}_{\mathbf{u}}(\mathbf{v}+\mathbf{w})$$

In Exercises \(39-46,\) find the unit vector that has the same direction as the vector \(\mathbf{v}\). $$\mathbf{v}=3 \mathbf{i}-4 \mathbf{j}$$

Test for symmetry and then graph each polar equation. $$r=\sin \theta \cos ^{2} \theta$$

Find the product of the complex numbers. Leave answers in polar form. $$\begin{array}{l} z_{1}=\cos \frac{\pi}{4}+i \sin \frac{\pi}{4} \\ z_{2}=\cos \frac{\pi}{3}+i \sin \frac{\pi}{3} \end{array}$$

Let $$\mathbf{u}=-\mathbf{i}+\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \text { and } \quad \mathbf{w}=-5 \mathbf{j}$$ Find each specified scalar or vector. $$\operatorname{proj}_{\mathbf{u}}(\mathbf{v}-\mathbf{w})$$