Chapter 9: Polar Coordinates, Vectors

Truck Pull At a county fair truck pull, two pickup trucks are attached to the back end of a monster truck as illustrated in the figure. One of the pickups pulls with a force of $2000$pounds and the other pulls with a force of $3000$pounds with an angle of $45$between them. With how much force must the monster truck pull in order to remain unmoved?

[Hint: Find the resultant force of the two trucks.]

The tests for symmetry given on page 574 are sufficient, but

not necessary. Explain what this means.

use the vectors in the figure at the right to graph each of the following vectors

v+w

Match each point in polar coordinates with either A,B,C or D on the graph.

$(2,-\frac{11\mathrm{\pi }}{6})$

Find the exact value of${\sin }^{-1}\left(-\frac{1}{2}\right)$.

Every nonzero complex number has exactly _______ distinct cube roots.

To test if the graph of a polar equation may be symmetric with respect to the polar axis, replace $\theta$by ________.

In Problems 7–16,

(a) find the dot product $v·w$;

(b) find the angle between v and w;

(c) state whether the vectors are parallel, orthogonal, or neither.

$$\begin{gathered} v=2i+j \\ w=i-2j \end{gathered}$$

In Problems $7-14$, find the value of each determinant.

$\left|\begin{array}{cc}6& 5\\ -2& -1\end{array}\right|$

The variables r and u represent polar coordinates. (a) Write each polar equation as an equation in rectangular

coordinates (x, y). (b) Identify the equation and graph it.

$\theta =\frac{\pi }{4}$