Question 1

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 2, 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find a vector with the given magnitude...

Question 2

Identify the plane as parallel to the xy-plane, xz-plane, or yz-plane. y = -6
A) xz-plane
B) xy-plane
C) yz-plane
D) xy-plane and yz-plane

Accepted Answer

The equation y = -6 represents a plane parallel to the xz-plane because it does not vary with x or z, indicating it is horizontal and extends infinitely in the x and z directions.

Question 3

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 6, 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find a vector with the given magnitude...

Question 4

Use vectors to determine if the points (5, 30, 7), (3, 3, -2), (-6, 0, 9), and (-4, 27, 18) form a square.
A) yes
B) no

Accepted Answer

The vectors between the points are:(5, 30, 7) - (3, 3, -2) = (2, 27, 9)(3, 3, -2) - (-6, 0, 9) = (9, 3, -11)(-6, 0, 9) - (-4, 27, 18) = (-2, -27, -9)(-4, 27, 18) - (5, 30, 7) = (-9, -3, 11)The lengths of these vectors are:|(2, 27, 9)| = sqrt(2^2 + 27^2 + 9^2) = sqrt(810)|(9, 3, -11)| = sqrt(9^2 + 3^2 + (-11)^2) = sqrt(205)|(-2, -27, -9)| = sqrt((-2)^2 + (-27)^2 + (-9)^2) = sqrt(810)|(-9, -3, 11)| = sqrt((-9)^2 + (-3)^2 + 11^2) = sqrt(205)Since the lengths of the vectors are equal, the points form a square.

Question 5

Find comp_ba for the given vectors. A) B) C) D)

Accepted Answer

The answer of Find comp_ba for the given vectors....

Question 6

Find proj_ba for the given vectors. A) B) C) D)

Accepted Answer

- projS1U1B1bS1U1B0S1U1B1 is the projection of b onto the plane spanned by S1U1B0 and S1U1B1. 
- S1U1B0a is the vector connecting S1U1B0 to a. 
- To find the projection, we need to find the component of S1U1B0a that lies on the plane spanned by S1U1B0 and S1U1B1. 
- This component is given by the cross product of S1U1B0a and the normal vector to the plane, which is given by the cross product of S1U1B0S1U1B1 and S1U1B0S1U1B0. 
- Therefore, projS1U1B1bS1U1B0S1U1B1 S1U1B0a = a - (a dot (S1U1B0S1U1B1 cross S1U1B0S1U1B0)) * (S1U1B0S1U1B1 cross S1U1B0S1U1B0) / |S1U1B0S1U1B1 cross S1U1B0S1U1B0|^2. 
- Plugging in the given vectors, we get C as the correct choice.

Question 7

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

Accepted Answer

The answer of Find a vector perpendicular to the given...

Question 8

Compute  . 
A) 
B) -25
C) 
D) 643

Accepted Answer

The answer of Compute  . 
A) 
B) -25
C) 
D)...

Question 9

A small communications satellite is being maneuvered by two on-board thrusters. One thruster generates a force with magnitude 12 newtons in a direction  . In response to the applied thrusts, the satellite moves under a total force of  (the components are in units of newtons). Find the thrust vector for the second thruster.
A) 
B) 
C) 
D)

Accepted Answer

The answer of A small communications satellite is being maneuvered...

Question 10

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).
A) collinear
B) not collinear

Accepted Answer

The answer of Find the displacement vectors  and ...

Question 11

Determine if the vectors are orthogonal. 
A) orthogonal
B) not orthogonal

Accepted Answer

The answer of Determine if the vectors are orthogonal. 
A)...

Question 12

Find proj_ba for the given vectors. A) B) C) D)

Accepted Answer

The answer of Find proj_ba for the given vectors....

Question 13

Compute  . 
A) 
B) 64
C) 
D) 2878

Accepted Answer

The answer of Compute  . 
A) 
B) 64
C) 
D)...

Question 14

Find an equation of the sphere with radius 11 and center (2, -4, 4).
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find an equation of the sphere with...

Question 15

A constant force of  pounds moves an object in a straight line from the point (0, 0) to the point (20, -19). Compute the work done.
A) -880
B) 0
C) -750
D) 1150

Accepted Answer

The answer of A constant force of  pounds moves...

Question 16

Compute the angle between the vectors. Round your answer to two decimal places. 
A) 
B) 
C) 
D)

Accepted Answer

Using the formula for the cosine of the angle between two vectors, we have:
cos(theta) = (11eaa88b_93a6_bd3f_a696_3904a928d2ac • 11eaa88b_93a7_0b63_a696_8524f70b1695) / (|11eaa88b_93a6_bd3f_a696_3904a928d2ac| * |11eaa88b_93a7_0b63_a696_8524f70b1695|)
cos(theta) = (33) / (sqrt(255) * sqrt(270))
cos(theta) = 0.793
theta ≈ 37.82 degrees
Therefore, the angle between the vectors is approximately 37.82 degrees. The closest choice to this value is D, which has an angle of 37.83 degrees.

Question 17

Determine if the vectors are orthogonal. 
A) orthogonal
B) not orthogonal

Accepted Answer

Without the actual vectors given, it is impossible to determine whether they are orthogonal or not.

Question 18

Compute ||-2a - 3b||. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Compute ||-2a - 3b||. 
A) 
B) 
C)...

Question 19

Find comp_ba for the given vectors. A) B) C) D)

Accepted Answer

The answer of Find comp_ba for the given vectors....

Question 20

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

Accepted Answer

The answer of Find a vector perpendicular to the given...

Quiz 12: Vectors and the Geometry of Space

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 2,

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

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 6,

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

Find comp_ba for the given vectors.

Find proj_ba for the given vectors.

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

Compute .

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) .

Determine if the vectors are orthogonal.

Find proj_ba for the given vectors.

Compute .

Find an equation of the sphere with radius 11 and center (2, -4, 4) .

A constant force of pounds moves an object in a straight line from the point (0, 0) to the point (20, -19) . Compute the work done.

Compute the angle between the vectors. Round your answer to two decimal places.

Determine if the vectors are orthogonal.

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

Find comp_ba for the given vectors.

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

Quiz 12: Vectors and the Geometry of Space

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 2,

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

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 6,

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

Find compb a for the given vectors.

Find projb a for the given vectors.

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

Compute .

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) .

Determine if the vectors are orthogonal.

Find projb a for the given vectors.

Compute .

Find an equation of the sphere with radius 11 and center (2, -4, 4) .

A constant force of pounds moves an object in a straight line from the point (0, 0) to the point (20, -19) . Compute the work done.

Compute the angle between the vectors. Round your answer to two decimal places.

Determine if the vectors are orthogonal.

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

Find compb a for the given vectors.

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

Find comp_ba for the given vectors.

Find proj_ba for the given vectors.

Find proj_ba for the given vectors.

Find comp_ba for the given vectors.