91Ó°ÊÓ

Describe the given set with a single equation or with a pair of equations. The plane through the point (3,-1,2) perpendicular to the a. \(x\) -axis b. \(y\) -axis c. z-axis

Sketch the surfaces in Exercises \(13-44\) $$y^{2}+z^{2}-x^{2}=1$$

Describe the given set with a single equation or with a pair of equations. The set of points in space equidistant from the origin and the point (0,2,0)

Find a vector of magnitude 3 in the direction opposite to the direction of \(\mathbf{v}=(1 / 2) \mathbf{i}-(1 / 2) \mathbf{j}-(1 / 2) \mathbf{k}\)

Write inequalities to describe the sets. The closed region bounded by the spheres of radius 1 and radius 2 centered at the origin. (Closed means the spheres are to be included. Had we wanted the spheres left out, we would have asked for the open region bounded by the spheres. This is analogous to the way we use closed and open to describe intervals: closed means endpoints included, open means endpoints left out. Closed sets include boundaries; open sets leave them out.)

Velocity An airplane is flying in the direction \(25^{\circ}\) west of north at \(800 \mathrm{km} / \mathrm{h} .\) Find the component form of the velocity of the airplane, assuming that the positive \(x\) -axis represents due east and the positive \(y\) -axis represents due north.

Vectors are drawn from the center of a regular \(n\) -sided polygon in the plane to the vertices of the polygon. Show that the sum of the vectors is zero. (Hint: What happens to the sum if you rotate the polygon about its center?)

Find an equation for the set of all points equidistant from the planes \(y=3\) and \(y=-1\).

Find an equation for the set of all points equidistant from the point (0,0,2) and the \(x y\) -plane.

Find the point equidistant from the points (0,0,0),(0,4,0) \((3,0,0),\) and (2,2,-3)