Chapter 9: Polar Coordinates, Vectors

Ground Speed and Direction of an Airplane An airplane has an airspeed of 500 kilometers per hour $(km/hr)$bearing$N45°E$ . The wind velocity is $60km/hr$in the direction $N30°W$. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?

The letters r and $\theta$represent polar coordinates. Write each equation using rectangular coordinates $(x,y)$.

$r=2$

Work

Find the work done in moving an object along a vector $u=3i+2j-5k$ if the applied force is $F=2i-j-k$. Use meters for distance and newtons for force.

$r=\tan \theta ,-\frac{\mathrm{\pi }}{2}<\theta <\frac{\mathrm{\pi }}{2}$(kappa curve)

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

$\left|\begin{array}{cc}-2& 5\\ 2& -3\end{array}\right|$

True or False Mass is an example of a vector.

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.

$r=5$

Describe the set of points $\left(x,y,z\right)$defined by the equation(s).

$x=0$

True or False The tests for symmetry in polar coordinates are necessary but not sufficient.

Graph the function$y=\sin \left|x\right|$