Question 1

Calculate the angle between a and b (correct to the nearest degree).   Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 2

Find an equation for the surface obtained by rotating the parabola   about the y-axis.

Accepted Answer

The answer of Find an equation for the surface obtained...

Question 3

Select the correct Answer for each question.
-Determine whether the given points are collinear.

Accepted Answer

A) Not collinear 
B) Collinear 
A) Not collinear 
B) Collinear

Question 4

Select the correct Answer: for each question.
-Find the center and the radius of the sphere that has the given equation.

Accepted Answer

A)    
B) ( -2, 4, 0), 20 
C)    
D) ( 2, -4, 0), 20 
A)    
B) ( -2, 4, 0), 20 
C)    
D) ( 2, -4, 0), 20

Question 5

Find   correct to three decimal places where

Accepted Answer

The answer of Find   correct to three decimal...

Question 6

Sketch the plane in a three-dimensional space represented by the equation.

Accepted Answer

The answer of Sketch the plane in a three-dimensional space...

Question 7

Find an equation for the surface obtained by rotating the parabola   about the y-axis.Select the correct Answer

Accepted Answer

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

Question 8

The tension T at each end of the chain has magnitude   and makes an angle   with the horizontal.What is the weight of the chain? Round the result to the nearest hundredth.

Accepted Answer

The answer of The tension T at each end of...

Question 9

Find the distance between the planes.

Accepted Answer

The answer of Find the distance between the planes. ...

Question 10

Select the correct Answer: for each question.
-Find an equation for the surface obtained by rotating the parabola   about the y-axis.

Accepted Answer

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

Question 11

Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a right triangle, both, or neither.Select the correct AnswerA (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)

Accepted Answer

A) 1, 1,   isosceles 
B) 1, 1,   oth 
C) 3, 2,   right 
D) 1, 2,   neither 
A) 1, 1,   isosceles 
B) 1, 1,   oth 
C) 3, 2,   right 
D) 1, 2,   neither

Question 12

Find parametric equations for the line through

Accepted Answer

The answer of Find parametric equations for the line through...

Question 13

Find the center and the radius of the sphere that has the given equation.

Accepted Answer

The answer of Find the center and the radius of...

Question 14

Select the correct Answer for each question.
-Find the distance between the planes.

Accepted Answer

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

Question 15

Select the correct Answer: for each question.
-Plot the given points in a three-dimensional coordinate system.

Accepted Answer

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

Question 16

Find the distance between the planes.

Accepted Answer

The answer of Find the distance between the planes. ...

Question 17

Find the distance from   to the xy-planes.

Accepted Answer

The answer of Find the distance from   to...

Question 18

Find the cross product

Accepted Answer

The answer of Find the cross product   ...

Question 19

Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.

Accepted Answer

The answer of Find the volume of the parallelepiped with...

Question 20

Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a right triangle, both, or neither.Select the correct AnswerA (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)

Accepted Answer

A) 1, 2,   neither 
B) 1, 1,   isosceles 
C) 1, 1,   both 
D) 3, 2,   right 
A) 1, 2,   neither 
B) 1, 1,   isosceles 
C) 1, 1,   both 
D) 3, 2,   right

Calculate the angle between a and b (correct to the nearest degree). Select the correct Answer

Find an equation for the surface obtained by rotating the parabola about the y-axis.

Select the correct Answer for each question. -Determine whether the given points are collinear.

Select the correct Answer: for each question. -Find the center and the radius of the sphere that has the given equation.

Find correct to three decimal places where

Sketch the plane in a three-dimensional space represented by the equation.

Find an equation for the surface obtained by rotating the parabola about the y-axis.Select the correct Answer

The tension T at each end of the chain has magnitude and makes an angle with the horizontal.What is the weight of the chain? Round the result to the nearest hundredth.

Find the distance between the planes.

Select the correct Answer: for each question. -Find an equation for the surface obtained by rotating the parabola about the y-axis.

Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a right triangle, both, or neither.Select the correct AnswerA (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)

Find parametric equations for the line through

Find the center and the radius of the sphere that has the given equation.

Select the correct Answer for each question. -Find the distance between the planes.

Select the correct Answer: for each question. -Plot the given points in a three-dimensional coordinate system.

Find the distance between the planes.

Find the distance from to the xy-planes.

Find the cross product

Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.

Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a right triangle, both, or neither.Select the correct AnswerA (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

Exam 12: Vectors and the Geometry of Space

Calculate the angle between a and b (correct to the nearest degree). Select the correct Answer

Find an equation for the surface obtained by rotating the parabola about the y-axis.

Select the correct Answer for each question. -Determine whether the given points are collinear.

Select the correct Answer: for each question. -Find the center and the radius of the sphere that has the given equation.

Find correct to three decimal places where

Sketch the plane in a three-dimensional space represented by the equation.

Find an equation for the surface obtained by rotating the parabola about the y-axis.Select the correct Answer

The tension T at each end of the chain has magnitude and makes an angle with the horizontal.What is the weight of the chain? Round the result to the nearest hundredth.

Find the distance between the planes.

Select the correct Answer: for each question. -Find an equation for the surface obtained by rotating the parabola about the y-axis.

Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a right triangle, both, or neither.Select the correct AnswerA (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)

Find parametric equations for the line through

Find the center and the radius of the sphere that has the given equation.

Select the correct Answer for each question. -Find the distance between the planes.

Select the correct Answer: for each question. -Plot the given points in a three-dimensional coordinate system.

Find the distance between the planes.

Find the distance from to the xy-planes.

Find the cross product

Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.

Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a right triangle, both, or neither.Select the correct AnswerA (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters