Question 1

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

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 consisting of all points P for which the distance from P to the x-axis is three times the distance from P to the yz-plane.

Accepted Answer

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

Question 3

Find   .

Accepted Answer

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

Question 4

Find the distance from   to the xy-planes.

Accepted Answer

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

Question 5

Find the derivative of the vector function.

Accepted Answer

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

Question 6

Suppose you start at the origin,move along the x-axis a distance of 6 units in the positive direction,and then move downward a distance of 1 units.What are the coordinates of your position?

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

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

Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is three times the distance from P to the yz-plane.

Find .

Find the distance from to the xy-planes.

Find the derivative of the vector function.

Suppose you start at the origin,move along the x-axis a distance of 6 units in the positive direction,and then move downward a distance of 1 units.What are the coordinates of your position?

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

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)

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Exam 10: Ectors and the Geometry of Space

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

Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is three times the distance from P to the yz-plane.

Find .

Find the distance from to the xy-planes.

Find the derivative of the vector function.

Suppose you start at the origin,move along the x-axis a distance of 6 units in the positive direction,and then move downward a distance of 1 units.What are the coordinates of your position?

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

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)

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters