Question 1

Find the distance from   to the xy-planes.Select the correct Answer

Accepted Answer

A) 8 
B) 16 
C) 10 
D) 2 
E) 4   
A) 8 
B) 16 
C) 10 
D) 2 
E) 4

Question 2

Reduce the equation to one of the standard forms.

Accepted Answer

The answer of Reduce the equation to one of the...

Question 3

Select the correct Answer: for each question.
-Determine whether the given points are collinear.A (2, 3, 2), B (-4, 0, 5), and C (4, 4, 1)

Accepted Answer

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

Question 4

Find the unit vectors that are parallel to the tangent line to the curve   at the point

Accepted Answer

The answer of Find the unit vectors that are parallel...

Question 5

Find the values of x such that the vectors   are orthogonal.Select the correct Answer

Accepted Answer

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

Question 6

Identify the planes that are perpendicular.Select the correct Answer

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Write inequalities to describe the solid rectangular box in the first octant bounded by the planes

Accepted Answer

The answer of Write inequalities to describe the solid rectangular...

Question 10

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 11

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.

Accepted Answer

The answer of Draw a rectangular box with the origin...

Question 12

Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

Accepted Answer

The answer of Find a nonzero vector orthogonal to the...

Question 13

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 14

Find correct to three decimal places where

Accepted Answer

The answer of Find correct to three decimal places where...

Question 15

Find the center and radius of the sphere.Select the correct Answer

Accepted Answer

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

Question 16

Select the correct Answer for each question.
-Find the cross product

Accepted Answer

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

Question 17

Find an equation of the sphere that passes through the point   and has center

Accepted Answer

The answer of Find an equation of the sphere that...

Question 18

Calculate the given quantities if

Accepted Answer

The answer of Calculate the given quantities if  ...

Question 19

Select the correct Answer: for each question.
-Find the distance between the point   and the plane   Round yourAnswer to two decimal place.

Accepted Answer

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

Question 20

Find an equation of the plane that passes through the line of intersection of the planes   and   is perpendicular to the plane

Accepted Answer

The answer of Find an equation of the plane that...

Find the distance from to the xy-planes.Select the correct Answer

Reduce the equation to one of the standard forms.

Select the correct Answer: for each question. -Determine whether the given points are collinear.A (2, 3, 2), B (-4, 0, 5), and C (4, 4, 1)

Find the unit vectors that are parallel to the tangent line to the curve at the point

Find the values of x such that the vectors are orthogonal.Select the correct Answer

Identify the planes that are perpendicular.Select the correct Answer

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

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

Write inequalities to describe the solid rectangular box in the first octant bounded by the planes

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

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.

Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

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

Find correct to three decimal places where

Find the center and radius of the sphere.Select the correct Answer

Select the correct Answer for each question. -Find the cross product

Find an equation of the sphere that passes through the point and has center

Calculate the given quantities if

Select the correct Answer: for each question. -Find the distance between the point and the plane Round yourAnswer to two decimal place.

Find an equation of the plane that passes through the line of intersection of the planes and is perpendicular to the plane

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

Find the distance from to the xy-planes.Select the correct Answer

Reduce the equation to one of the standard forms.

Select the correct Answer: for each question. -Determine whether the given points are collinear.A (2, 3, 2), B (-4, 0, 5), and C (4, 4, 1)

Find the unit vectors that are parallel to the tangent line to the curve at the point

Find the values of x such that the vectors are orthogonal.Select the correct Answer

Identify the planes that are perpendicular.Select the correct Answer

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

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

Write inequalities to describe the solid rectangular box in the first octant bounded by the planes

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

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.

Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

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

Find correct to three decimal places where

Find the center and radius of the sphere.Select the correct Answer

Select the correct Answer for each question. -Find the cross product

Find an equation of the sphere that passes through the point and has center

Calculate the given quantities if

Select the correct Answer: for each question. -Find the distance between the point and the plane Round yourAnswer to two decimal place.

Find an equation of the plane that passes through the line of intersection of the planes and is perpendicular to the plane

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