Question 1

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

Accepted Answer

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

Question 2

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 3

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 4

Determine whether the given points are collinear.Select the correct Answer

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Find parametric equations for the line through the point   that is parallel to the plane   and perpendicular to the line   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 length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a right triangle, both, or neither.A (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)

Accepted Answer

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

Question 8

Which of the given lines is parallel to the line

Accepted Answer

The answer of Which of the given lines is parallel...

Question 9

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

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 10

Select the correct Answer for each question.
-Reduce the equation to one of the standard forms.

Accepted Answer

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

Question 11

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

Accepted Answer

The answer of An ellipsoid is created by rotating the...

Question 12

Select the correct Answer: for each question.
-Suppose you start at the origin, move along the x-axis a distance of   units in the positive direction, and then move downward a distance of   units.What are the coordinates of your position?

Accepted Answer

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

Question 13

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

Accepted Answer

The answer of Find the distance (correct to two decimal...

Question 14

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 15

Select the correct Answer: for each question.
-Find an equation of the sphere with center   that touches the xy-plane.

Accepted Answer

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

Question 16

Find the midpoint of the line segment joining the given points.Select the correct Answer(3, 1, 4) and (5, -1, 6)

Accepted Answer

A)    
B)    
C) (4, 0, 5) 
D)    
A)    
B)    
C) (4, 0, 5) 
D)

Question 17

Select the correct Answer: for each question.
-Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

Accepted Answer

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

Question 18

Find an equation for the surface consisting of all points that are equidistant from the point   and the plane

Accepted Answer

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

Question 19

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

Accepted Answer

The answer of Let   and let u be...

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

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

Determine whether the given points are collinear.Select the correct Answer

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

Find parametric equations for the line through the point that is parallel to the plane and perpendicular to the line Select the correct Answer

Select the correct Answer for each question. -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.A (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)

Which of the given lines is parallel to the line

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

Select the correct Answer for each question. -Reduce the equation to one of the standard forms.

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

Select the correct Answer: for each question. -Suppose you start at the origin, move along the x-axis a distance of units in the positive direction, and then move downward a distance of units.What are the coordinates of your position?

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

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

Select the correct Answer: for each question. -Find an equation of the sphere with center that touches the xy-plane.

Find the midpoint of the line segment joining the given points.Select the correct Answer(3, 1, 4) and (5, -1, 6)

Select the correct Answer: for each question. -Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

Find an equation for the surface consisting of all points that are equidistant from the point and the plane

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

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

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Exam 12: Vectors and the Geometry of Space

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

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

Determine whether the given points are collinear.Select the correct Answer

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

Find parametric equations for the line through the point that is parallel to the plane and perpendicular to the line Select the correct Answer

Select the correct Answer for each question. -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.A (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)

Which of the given lines is parallel to the line

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

Select the correct Answer for each question. -Reduce the equation to one of the standard forms.

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

Select the correct Answer: for each question. -Suppose you start at the origin, move along the x-axis a distance of units in the positive direction, and then move downward a distance of units.What are the coordinates of your position?

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

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

Select the correct Answer: for each question. -Find an equation of the sphere with center that touches the xy-plane.

Find the midpoint of the line segment joining the given points.Select the correct Answer(3, 1, 4) and (5, -1, 6)

Select the correct Answer: for each question. -Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

Find an equation for the surface consisting of all points that are equidistant from the point and the plane

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

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