Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

The answer of Find the length of the median of...

Question 3

Find the point of intersection.

Accepted Answer

The answer of Find the point of intersection.  ...

Question 4

Find the distance between the point   and the plane   Round your answer to two decimal place.

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D)    
E)

Question 5

Find an equation of the set of all points equidistant from the points   and

Accepted Answer

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D)    
E)    
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E)

Question 6

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 7

Find an equation for the surface obtained by rotating the line   about the x-axis.

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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B)    
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E) none of these 
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E) none of these

Question 10

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

Question 11

Classify the surface.

Accepted Answer

A) A circular paraboloid with vertex   and axis the z-axis. 
B) A hyperboloid of one sheet with center   and axis parallel to the z-axis. 
C) A cone with axis parallel to the z-axis and vertex   . 
A) A circular paraboloid with vertex   and axis the z-axis. 
B) A hyperboloid of one sheet with center   and axis parallel to the z-axis. 
C) A cone with axis parallel to the z-axis and vertex   .

Question 12

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

Accepted Answer

The answer of Find the equation of the line through...

Question 13

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

Accepted Answer

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B)    
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B)    
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D)    
E)

Question 14

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

Accepted Answer

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

Question 15

Find the work done by a force   that moves an object from the point   to the point   along a straight line. The distance is measured in meters and the force in newtons.

Accepted Answer

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

Question 16

Find the midpoint of the line segment joining the given points. (-5, 0, 2) and (-3, -2, 4)

Accepted Answer

A) ( -4 ,-1 ,3 ) 
B) (   ,   ,   ) 
C) (   ,   ,   ) 
D) (   ,   ,   ) 
A) ( -4 ,-1 ,3 ) 
B) (   ,   ,   ) 
C) (   ,   ,   ) 
D) (   ,   ,   )

Question 17

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

Accepted Answer

The answer of Write an inequality to describe the half-space...

Question 18

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

Accepted Answer

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

Question 19

The tension T at each end of the chain has magnitude   N 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 20

Find the values of x such that the vectors   and   are orthogonal.

Accepted Answer

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

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

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

Find the point of intersection.

Find the distance between the point and the plane Round your answer to two decimal place.

Find an equation of the set of all points equidistant from the points and

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 an equation for the surface obtained by rotating the line about the x-axis.

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

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

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)

Classify the surface.

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

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

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

Find the work done by a force that moves an object from the point to the point along a straight line. The distance is measured in meters and the force in newtons.

Find the midpoint of the line segment joining the given points. (-5, 0, 2) and (-3, -2, 4)

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

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

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

Find the values of x such that the vectors and are orthogonal.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

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

Final Exam

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Exam 12: Vectors and the Geometry of Space

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

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

Find the point of intersection.

Find the distance between the point and the plane Round your answer to two decimal place.

Find an equation of the set of all points equidistant from the points and

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 an equation for the surface obtained by rotating the line about the x-axis.

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

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

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)

Classify the surface.

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

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

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

Find the work done by a force that moves an object from the point to the point along a straight line. The distance is measured in meters and the force in newtons.

Find the midpoint of the line segment joining the given points. (-5, 0, 2) and (-3, -2, 4)

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

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

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

Find the values of x such that the vectors and are orthogonal.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

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

Final Exam

Filters