Question 1

Find the vector with initial point A and terminal point B. A = (5, -4), B = (9, 5)

Accepted Answer

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

Question 2

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Accepted Answer

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

Question 3

Find an equation of the given plane. The plane containing the point   and perpendicular to the planes 7x + y - z = -5 and x - 6y - 4z = -3

Accepted Answer

A)  -10x + 27y - 43z = -9 
B)  -10x + 27y - 43z = -78 
C)  7x + y - z = 31 
D)  -10x + 27y - 43z = 416 
A)  -10x + 27y - 43z = -9 
B)  -10x + 27y - 43z = -78 
C)  7x + y - z = 31 
D)  -10x + 27y - 43z = 416 B

Question 4

Compute ||-4a - 3b||.

Accepted Answer

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

Question 5

Find two unit vectors orthogonal to the two given vectors.

Accepted Answer

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

Question 6

Determine whether the given lines are the same. x = 2 - 9t, y = -9 + 3t, z = 4 + 5t and x = 2 + 6t, y = -9 + 5t, z = 4 + 7t

Accepted Answer

A)  The lines are the same. 
B)  The lines are not the same. 
A)  The lines are the same. 
B)  The lines are not the same.

Question 7

Find a vector perpendicular to the given vector. Show all your work.

Accepted Answer

Answer may vary. Fin

Question 8

Identify the plane as parallel to the xy-plane, xz-plane, or yz-plane. y = -6

Accepted Answer

A)  xz-plane 
B)  xy-plane 
C)  yz-plane 
D)  xy-plane and yz-plane 
A)  xz-plane 
B)  xy-plane 
C)  yz-plane 
D)  xy-plane and yz-plane

Question 9

Identify the surface.

Accepted Answer

A)  hyperboloid of two sheets 
B)  cone 
C)  hyperboloid of one sheet 
D)  hyperbolic paraboloid 
A)  hyperboloid of two sheets 
B)  cone 
C)  hyperboloid of one sheet 
D)  hyperbolic paraboloid

Question 10

Find the distance between the given objects. The point   and the plane -7x + 8y - 5z = -8

Accepted Answer

A)    
B)    
C)  0 
D)    
A)    
B)    
C)  0 
D)

Question 11

Determine if the vectors are orthogonal.

Accepted Answer

A)  orthogonal 
B)  not orthogonal 
A)  orthogonal 
B)  not orthogonal

Question 12

Find compb a for the given vectors.

Accepted Answer

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

Question 13

Prove that projc(a + b) = projc a + projc b for any non-zero vectors a, b, and c.

Accepted Answer

Question 14

Determine if the lines are parallel, skew or intersect.

Accepted Answer

A)  parallel 
B)  skew 
C)  intersect 
A)  parallel 
B)  skew 
C)  intersect

Question 15

Use vectors to determine if the points (5, 30, 7), (3, 3, -2), (-6, 0, 9), and (-4, 27, 18) form a square.

Accepted Answer

A)  yes 
B)  no 
A)  yes 
B)  no

Question 16

If   ,   , and   for   and   , show that the point (x, y, z) lies on the upper half of the cone   . Show all your work.

Accepted Answer

@#IMG-DLM& Since @#IMG-DLM& is positive

Question 17

Find compb a for the given vectors.

Accepted Answer

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

Question 18

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Accepted Answer

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

Question 19

Find the indicated area. Area of the parallelogram with two adjacent sides formed by   and

Accepted Answer

A)    
B)  45 
C)  81 
D)    
A)    
B)  45 
C)  81 
D)

Question 20

Show that   . Show all of your work.

Accepted Answer

The answer of Show that   . Show all...

Find the vector with initial point A and terminal point B. A = (5, -4), B = (9, 5)

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Find an equation of the given plane. The plane containing the point and perpendicular to the planes 7x + y - z = -5 and x - 6y - 4z = -3

Compute ||-4a - 3b||.

Find two unit vectors orthogonal to the two given vectors.

Determine whether the given lines are the same. x = 2 - 9t, y = -9 + 3t, z = 4 + 5t and x = 2 + 6t, y = -9 + 5t, z = 4 + 7t

Find a vector perpendicular to the given vector. Show all your work.

Identify the plane as parallel to the xy-plane, xz-plane, or yz-plane. y = -6

Identify the surface.

Find the distance between the given objects. The point and the plane -7x + 8y - 5z = -8

Determine if the vectors are orthogonal.

Find comp_ba for the given vectors.

Prove that proj_c(a + b) = proj_c a + proj_c b for any non-zero vectors a, b, and c.

Determine if the lines are parallel, skew or intersect.

Use vectors to determine if the points (5, 30, 7), (3, 3, -2), (-6, 0, 9), and (-4, 27, 18) form a square.

If , , and for and , show that the point (x, y, z) lies on the upper half of the cone . Show all your work.

Find comp_ba for the given vectors.

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Find the indicated area. Area of the parallelogram with two adjacent sides formed by and

Show that . Show all of your work.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 12: Vectors and the Geometry of Space

Find the vector with initial point A and terminal point B. A = (5, -4), B = (9, 5)

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Find an equation of the given plane. The plane containing the point and perpendicular to the planes 7x + y - z = -5 and x - 6y - 4z = -3

Compute ||-4a - 3b||.

Find two unit vectors orthogonal to the two given vectors.

Determine whether the given lines are the same. x = 2 - 9t, y = -9 + 3t, z = 4 + 5t and x = 2 + 6t, y = -9 + 5t, z = 4 + 7t

Find a vector perpendicular to the given vector. Show all your work.

Identify the plane as parallel to the xy-plane, xz-plane, or yz-plane. y = -6

Identify the surface.

Find the distance between the given objects. The point and the plane -7x + 8y - 5z = -8

Determine if the vectors are orthogonal.

Find compb a for the given vectors.

Prove that projc(a + b) = projc a + projc b for any non-zero vectors a, b, and c.

Determine if the lines are parallel, skew or intersect.

Use vectors to determine if the points (5, 30, 7), (3, 3, -2), (-6, 0, 9), and (-4, 27, 18) form a square.

If , , and for and , show that the point (x, y, z) lies on the upper half of the cone . Show all your work.

Find compb a for the given vectors.

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Find the indicated area. Area of the parallelogram with two adjacent sides formed by and

Show that . Show all of your work.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Find comp_ba for the given vectors.

Prove that proj_c(a + b) = proj_c a + proj_c b for any non-zero vectors a, b, and c.

Find comp_ba for the given vectors.