Question 1

Compute ||-3a - 2b||.

Accepted Answer

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

Question 2

Compute a + b.

Accepted Answer

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

Question 3

If you apply a force of magnitude 39 pounds at the end of an 9-inch wrench at an angle of   to the wrench, find the magnitude of the torque applied to the bolt. Round to the nearest tenth of an inch-pound.

Accepted Answer

A)  25.3 in-lb 
B)  175.5 in-lb 
C)  14.6 in-lb 
D)  304.0 in-lb 
A)  25.3 in-lb 
B)  175.5 in-lb 
C)  14.6 in-lb 
D)  304.0 in-lb

Question 4

A certain lunar crater is shaped approximately as a paraboloid (see figure). The cross sections of the crater parallel to the lunar surface are circular, with a maximum radius of 80 meters. The depth of the crater is 16 meters. Find an equation for the surface of the crater. [Write your equation such that the bottom of the crater is located at (x, y, z) = (0, 0, 0). Assume the z-axis is perpendicular to the lunar surface.]

Accepted Answer

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

Question 5

If   find a vector   such that

Accepted Answer

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

Question 6

Determine if the lines are parallel, skew or intersect.

Accepted Answer

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

Question 7

Compute the cross product a × b.

Accepted Answer

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

Question 8

Compute   .

Accepted Answer

A)    
B)  64 
C)    
D)  2878 
A)    
B)  64 
C)    
D)  2878

Question 9

Use the cross product to determine the angle betweeen the vectors, assuming that   . Round to the nearest thousandth.

Accepted Answer

A)  1.571 
B)  0.467 
C)  0.735 
D)  0.835 
A)  1.571 
B)  0.467 
C)  0.735 
D)  0.835

Question 10

Find a vector with the given magnitude in the same direction as the given vector. magnitude 6, v = i - 5j

Accepted Answer

A)  6i - 30j 
B)    
C)    
D)  6i 
A)  6i - 30j 
B)    
C)    
D)  6i

Question 11

Find an equation of the plane containing the lines.

Accepted Answer

A)  -19x - 17y + 14z = -21 
B)  -19x + y + 14z = -183 
C)  3x - 5y - 2z = 71 
D)  The lines are skew. 
A)  -19x - 17y + 14z = -21 
B)  -19x + y + 14z = -183 
C)  3x - 5y - 2z = 71 
D)  The lines are skew.

Question 12

Find parametric equations of the line through   and   .

Accepted Answer

The answer of Find parametric equations of the line through...

Question 13

Find projb a for the given vectors.

Accepted Answer

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

Question 14

A constant force of   pounds moves an object in a straight line a distance of 15 feet, and the work done is 110 ft-lb. If the motion of the object started at the point (0, 0), find the coordinates of the final position of the object. [Assume that the final position is somewhere in the first quadrant of the coordinate system.]

Accepted Answer

A)    
B)    
C)    
D)  The final position cannot be determined. 
A)    
B)    
C)    
D)  The final position cannot be determined.

Question 15

Find the angle between the lines. Round to the nearest hundredth of a radian.

Accepted Answer

A)  1.86 
B)  0.29 
C)  2.85 
D)  0.76 
A)  1.86 
B)  0.29 
C)  2.85 
D)  0.76

Question 16

Use the Cauchy-Schwartz Inequality in n dimensions to show that   ,
where m is an odd natural number.

Accepted Answer

Cauchy-Schwartz Inequality: @#IMG-DLM& Let @#IMG-DLM& and @#IMG-DLM& .

Question 17

Write the given vector as the product of its magnitude and a unit vector. (Write the unit vector so that it is in the same direction as the given vector. This means that the signs of the components of the unit vector should be the same as the signs of the corresponding components of the given vector.) From   to

Accepted Answer

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

Question 18

Find the intersection of the planes. -9x - 8y - 8z = 74 and 8x - 5y + 3z = -21

Accepted Answer

A)  x = -2 - 16t, y = -2 + 91t, z = -5 + 19t 
B)  x = 16t, y = -91t, z = -19t 
C)  x = -2 - 64t, y = -2 - 37t, z = -5 + 109t 
D)  The planes are parallel. 
A)  x = -2 - 16t, y = -2 + 91t, z = -5 + 19t 
B)  x = 16t, y = -91t, z = -19t 
C)  x = -2 - 64t, y = -2 - 37t, z = -5 + 109t 
D)  The planes are parallel.

Question 19

Determine whether the vectors a and b are parallel.

Accepted Answer

A)  parallel 
B)  not parallel 
A)  parallel 
B)  not parallel

Question 20

Find the displacement vectors   and   and determine whether the points P = (8, 0, 4), Q = (0, -8, -4), and R = (5, -3, 1) are collinear (on the same line).

Accepted Answer

A)  collinear 
B)  not collinear 
A)  collinear 
B)  not collinear

Compute ||-3a - 2b||.

Compute a + b.

If you apply a force of magnitude 39 pounds at the end of an 9-inch wrench at an angle of to the wrench, find the magnitude of the torque applied to the bolt. Round to the nearest tenth of an inch-pound.

If find a vector such that

Determine if the lines are parallel, skew or intersect.

Compute the cross product a × b.

Compute .

Use the cross product to determine the angle betweeen the vectors, assuming that . Round to the nearest thousandth.

Find a vector with the given magnitude in the same direction as the given vector. magnitude 6, v = i - 5j

Find an equation of the plane containing the lines.

Find parametric equations of the line through and .

Find proj_ba for the given vectors.

Find the angle between the lines. Round to the nearest hundredth of a radian.

Use the Cauchy-Schwartz Inequality in n dimensions to show that , where m is an odd natural number.

Find the intersection of the planes. -9x - 8y - 8z = 74 and 8x - 5y + 3z = -21

Determine whether the vectors a and b are parallel.

Find the displacement vectors and and determine whether the points P = (8, 0, 4), Q = (0, -8, -4), and R = (5, -3, 1) are collinear (on the same line).

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

Compute ||-3a - 2b||.

Compute a + b.

If you apply a force of magnitude 39 pounds at the end of an 9-inch wrench at an angle of to the wrench, find the magnitude of the torque applied to the bolt. Round to the nearest tenth of an inch-pound.

If find a vector such that

Determine if the lines are parallel, skew or intersect.

Compute the cross product a × b.

Compute .

Use the cross product to determine the angle betweeen the vectors, assuming that . Round to the nearest thousandth.

Find a vector with the given magnitude in the same direction as the given vector. magnitude 6, v = i - 5j

Find an equation of the plane containing the lines.

Find parametric equations of the line through and .

Find projb a for the given vectors.

Find the angle between the lines. Round to the nearest hundredth of a radian.

Use the Cauchy-Schwartz Inequality in n dimensions to show that , where m is an odd natural number.

Find the intersection of the planes. -9x - 8y - 8z = 74 and 8x - 5y + 3z = -21

Determine whether the vectors a and b are parallel.

Find the displacement vectors and and determine whether the points P = (8, 0, 4), Q = (0, -8, -4), and R = (5, -3, 1) are collinear (on the same line).

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 proj_ba for the given vectors.