Exam 12: Vectors and the Geometry of Space

Let and let u be a vector with length that starts at the origin and rotates in the xy - plane.Find the maximum value of the length of the vector Select the correct Answer

Write an inequality to describe the half-space consisting of all points to the left of a plane parallel to the -plane and units to the right of it.

Find the distance between the planes.

Find the length of the median of side AB of the triangle with vertices

An ellipsoid is created by rotating the ellipse about the x-axis.Find the equation of the ellipsoid.

Find an equation of the set of all points equidistant from the points Select the correct Answer

Draw a rectangular box with the origin and as opposite vertices and with its faces parallel to the coordinate planes.Find the length of the diagonal of the box.

Velocities have both direction and magnitude and thus are vectors.The magnitude of a velocity vector is called speed.Suppose that a wind is blowing from the direction N W at a speed of km/h.(This means that the direction from which the wind blows is west of the northerly direction.) A pilot is steering a plane in the direction N E at an airspeed (speed in still air) of The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind.The ground speed of the plane is the magnitude of the resultant.Find the ground speed of the plane.Round the result to the nearest hundredth.

Write an inequality to describe the half-space consisting of all points to the left of a plane parallel to the to the right of it.

Find an equation of the plane with x-intercept y-intercept and

Find, correct to the nearest degree, the angle between the planes.Select the correct Answer

Two forces with magnitudes 8 lb and 12 lb act on an object at a point P as shown in the figure.Find the magnitude of the resultant force F acting at P.Round the result to the nearest tenth.

Classify the surface.Select the correct Answer

Find, correct to the nearest degree, the angle between the planes.Select the correct Answer

Write an inequality to describe the region consisting of all points between (but not on) the spheres of radius entered at the origin.

Find the equation of the line through and perpendicular to the plane

Select the correct Answer: for each question. -Find, correct to the nearest degree, the angle between the planes.

Find that the midpoint of the line segment from

Find the distance (correct to two decimal places) between the given parallel planes.

Write inequalities to describe the solid upper hemisphere of the sphere of radius centered at the origin.