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Exam 10: Vectors and the Geometry of Space

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Exam 1: Functions and Limits54 Questionsadd course
Exam 2: Derivatives50 Questionsadd course
Exam 3: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions43 Questionsadd course
Exam 4: Applications of Differentiation68 Questionsadd course
Exam 5: Integrals33 Questionsadd course
Exam 6: Techniques of Integration46 Questionsadd course
Exam 7: Applications of Integration69 Questionsadd course
Exam 8: Series51 Questionsadd course
Exam 9: Parametric Equations and Polar Coordinates30 Questionsadd course
Exam 10: Vectors and the Geometry of Space68 Questionsadd course
Exam 11: Partial Derivatives73 Questionsadd course
Exam 12: Multiple Integrals59 Questionsadd course
Exam 13: Vector Calculus54 Questionsadd course
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The tension T at each end of the chain has magnitude 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. N and makes an angle 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. with the horizontal. What is the weight of the chain? Round the result to the nearest hundredth. 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.

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Question 21

Find Find . . Find .

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Question 22

A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of a. Find the range of the projectile. b. What is the maximm height attained by the projectile? c. What is the speed of the projectile at impact? Round your answers to the nearest integer. a. Find the range of the projectile. b. What is the maximm height attained by the projectile? c. What is the speed of the projectile at impact? Round your answers to the nearest integer.

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Question 23

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

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Question 24

Find the velocity, acceleration, and speed of an object with position function Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors. for Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors. Sketch the path of the object and its velocity and acceleration vectors.

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Question 25

Write an inequality to describe the region consisting of all points between (but not on) the spheres of radius Write an inequality to describe the region consisting of all points between (but not on) the spheres of radius and centered at the origin. and Write an inequality to describe the region consisting of all points between (but not on) the spheres of radius and centered at the origin. centered at the origin.

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Question 26

Let Let .Find the domain of . .Find the domain of Let .Find the domain of . .

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Question 27

Find the velocity and position vectors of an object with acceleration Find the velocity and position vectors of an object with acceleration initial velocity and initial position initial velocity Find the velocity and position vectors of an object with acceleration initial velocity and initial position and initial position Find the velocity and position vectors of an object with acceleration initial velocity and initial position

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Question 28

Find the derivative of the vector function. Find the derivative of the vector function.

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Question 29

A force with magnitude A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. N acts directly upward from the xy-plane on an object with mass A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. kg. The object starts at the origin with initial velocity A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. . Find its position function.

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Question 30

Find the speed of a particle with the given position function. Find the speed of a particle with the given position function.

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Question 31

Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as shown. Let Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as shown. Let ft, ft, , lb. ft, Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as shown. Let ft, ft, , lb. ft, Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as shown. Let ft, ft, , lb. , Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as shown. Let ft, ft, , lb. lb. Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as shown. Let ft, ft, , lb.

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Question 32

Find parametric equations for the line through Find parametric equations for the line through and parallel to the vector and parallel to the vector Find parametric equations for the line through and parallel to the vector

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Question 33

At what point on the curve At what point on the curve is the normal plane parallel to the plane ? is the normal plane parallel to the plane At what point on the curve is the normal plane parallel to the plane ? ?

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Question 34

Find a vector function that represents the curve of intersection of the two surfaces: The circular cylinder Find a vector function that represents the curve of intersection of the two surfaces: The circular cylinder and the parabolic cylinder . and the parabolic cylinder Find a vector function that represents the curve of intersection of the two surfaces: The circular cylinder and the parabolic cylinder . .

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Question 35

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

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Question 36

Which of the given lines is parallel to the line Which of the given lines is parallel to the line

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Question 37

Write inequalities to describe the solid upper hemisphere of the sphere of radius Write inequalities to describe the solid upper hemisphere of the sphere of radius centered at the origin. centered at the origin.

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Question 38

For the curve given by For the curve given by , find the unit normal vector. , find the unit normal vector. For the curve given by , find the unit normal vector.

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Question 39

Find the scalar tangential and normal components of acceleration of a particle with position vector Find the scalar tangential and normal components of acceleration of a particle with position vector

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Question 40
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