Question 1

Identify the following quadric surface.

Accepted Answer

A)  ellipsoid 
B)  elliptic cone 
C)  elliptic paraboloid 
D)  hyperboloid of one sheet 
E)  hyperboloid of two sheets 
A)  ellipsoid 
B)  elliptic cone 
C)  elliptic paraboloid 
D)  hyperboloid of one sheet 
E)  hyperboloid of two sheets

Question 2

Identify the following quadric surface.

Accepted Answer

A)  hyperboloid of one sheet 
B)  elliptic cone 
C)  elliptic paraboloid 
D)  hyperboloid of two sheets 
E)  hyperbolic paraboloid 
A)  hyperboloid of one sheet 
B)  elliptic cone 
C)  elliptic paraboloid 
D)  hyperboloid of two sheets 
E)  hyperbolic paraboloid

Question 3

Find the magnitude of the vector v given its initial and terminal points. Round your answer to four decimal places. Initial point: (3, -3, -4)
Terminal point: (8, -7, -1)

Accepted Answer

A)    or 7.2801 
B)    or 7.6158 
C)    or 7.0711 
D)    or 4.3589 
E)    or 7.8102 
A)    or 7.2801 
B)    or 7.6158 
C)    or 7.0711 
D)    or 4.3589 
E)    or 7.8102

Question 4

Find the equation of the surface satisfying the conditions, and identify the surface. The set of points equidistant from the point (-4, 3, 2 ) and the plane   .

Accepted Answer

A)    , an elliptic paraboloid 
B)    , a sphere 
C)    , a hyperbolic paraboloid 
D)    , a sphere 
E)    , a hyperbolic paraboloid 
A)    , an elliptic paraboloid 
B)    , a sphere 
C)    , a hyperbolic paraboloid 
D)    , a sphere 
E)    , a hyperbolic paraboloid

Question 5

Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve
Coordinate Plane
Axis of Revolution     -plane   -plane

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Determine whether the lines given below intersect, and, if so, find the point of intersection.

Accepted Answer

A)  The lines are parallel. 
B)  The lines intersect at   . 
C)  The lines intersect at   . 
D)  The lines intersect at   . 
E)  The lines are not parallel but do not intersect. 
A)  The lines are parallel. 
B)  The lines intersect at   . 
C)  The lines intersect at   . 
D)  The lines intersect at   . 
E)  The lines are not parallel but do not intersect.

Question 7

Find the standard equation of the sphere with center at   and tangent to the yz-plane.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Find the vector v whose initial and terminal points are given below. (6,2), (2,-2)

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Determine whether the lines given below intersect, and, if so, find the point of intersection.

Accepted Answer

A)  The lines intersect at   . 
B)  The lines are parallel. 
C)  The lines intersect at   . 
D)  The lines intersect at   . 
E)  The lines are not parallel but do not intersect. 
A)  The lines intersect at   . 
B)  The lines are parallel. 
C)  The lines intersect at   . 
D)  The lines intersect at   . 
E)  The lines are not parallel but do not intersect.

Question 10

Identify the following quadric surface.

Accepted Answer

A)  elliptic paraboloid 
B)  elliptic cone 
C)  hyperboloid of two sheets 
D)  hyperboloid of one sheet 
E)  ellipsoid 
A)  elliptic paraboloid 
B)  elliptic cone 
C)  hyperboloid of two sheets 
D)  hyperboloid of one sheet 
E)  ellipsoid

Question 11

Given   and   find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Find the vector v with the given magnitude ||v|| = 277 and the same direction as   .

Accepted Answer

A)   
B)   
C)   
D)   
E)   
A)   
B)   
C)   
D)   
E)

Question 13

Suppose a gun with a muzzle velocity of 1300 feet per second is fired at an angle of   above the horizontal. Find the horizontal component of the velocity. Round your answer to two decimal places.

Accepted Answer

A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
E)    ft/sec 
A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
E)    ft/sec

Question 14

Given   and   , find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Sketch the graph of the cross product of the unit vector   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Suppose a plane flies at a constant groundspeed of 100 miles per hour due east and encounters a 40 mile-per-hour wind from the northwest. Both the airspeed and the compass direction must change to for the plane to maintain its groundspeed and eastward direction. Find the airspeed to maintain its groundspeed and eastward direction. Round your answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve   in the yz-plane about the z-axis. The bushing has a hole of 1 centimeter in diameter through its center and parallel to the axis of revolution. All measurements are in centimeters and the bushing is set on the xy-plane. Find the volume of the rubber bushing. Round your answer to two decimal places. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Given   and   find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Find the area of the parallelogram that has the given vectors   and   as adjacent sides.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Identify the following quadric surface.

Identify the following quadric surface.

Find the magnitude of the vector v given its initial and terminal points. Round your answer to four decimal places. Initial point: (3, -3, -4) Terminal point: (8, -7, -1)

Find the equation of the surface satisfying the conditions, and identify the surface. The set of points equidistant from the point (-4, 3, 2 ) and the plane .

Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve Coordinate Plane Axis of Revolution -plane -plane

Determine whether the lines given below intersect, and, if so, find the point of intersection.

Find the standard equation of the sphere with center at and tangent to the yz-plane.

Find the vector v whose initial and terminal points are given below. (6,2), (2,-2)

Determine whether the lines given below intersect, and, if so, find the point of intersection.

Identify the following quadric surface.

Given and find .

Find the vector v with the given magnitude ||v|| = 277 and the same direction as .

Suppose a gun with a muzzle velocity of 1300 feet per second is fired at an angle of above the horizontal. Find the horizontal component of the velocity. Round your answer to two decimal places.

Given and , find .

Sketch the graph of the cross product of the unit vector .

Given and find .

Find the area of the parallelogram that has the given vectors and as adjacent sides.

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 11: Vectors and the Geometry of Space

Identify the following quadric surface.

Identify the following quadric surface.

Find the magnitude of the vector v given its initial and terminal points. Round your answer to four decimal places. Initial point: (3, -3, -4) Terminal point: (8, -7, -1)

Find the equation of the surface satisfying the conditions, and identify the surface. The set of points equidistant from the point (-4, 3, 2 ) and the plane .

Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve Coordinate Plane Axis of Revolution -plane -plane

Determine whether the lines given below intersect, and, if so, find the point of intersection.

Find the standard equation of the sphere with center at and tangent to the yz-plane.

Find the vector v whose initial and terminal points are given below. (6,2), (2,-2)

Determine whether the lines given below intersect, and, if so, find the point of intersection.

Identify the following quadric surface.

Given and find .

Find the vector v with the given magnitude ||v|| = 277 and the same direction as .

Suppose a gun with a muzzle velocity of 1300 feet per second is fired at an angle of above the horizontal. Find the horizontal component of the velocity. Round your answer to two decimal places.

Given and , find .

Sketch the graph of the cross product of the unit vector . ​

Given and find .

Find the area of the parallelogram that has the given vectors and as adjacent sides.

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Sketch the graph of the cross product of the unit vector .