Question 1

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.) 
A) 
B) 
C) 
D)

Accepted Answer

To find the unit vector, we need to divide the given vector by its magnitude. The magnitude of the vector is the square root of the sum of the squares of its components:
magnitude = sqrt(11^2 + (-202)^2 + 426^2 + (-468)^2) = 697
Now we can divide each component of the given vector by the magnitude to get the corresponding component of the unit vector:
u = (11/697, -202/697, 426/697, -468/697)
The signs of the components of the unit vector should be the same as the signs of the corresponding components of the given vector, which means that option C is the best choice.

Question 2

Illustrate the difference a - b graphically. a = -i + 4j; b = -3i + 3j 
A) 
B) 
C) 
D)

Accepted Answer

C

Question 3

Find the vector with initial point A and terminal point B. A = (4, 2), B = (-3, -7)
A) 
B) 
C) 
D)

Accepted Answer

D

Question 4

Find two unit vectors parallel to the given vector. From  to 
A)  
B)  
C)  
D)

Accepted Answer

The answer of Find two unit vectors parallel to the...

Question 5

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

Accepted Answer

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

Question 6

The motor of a small boat produces a speed of 3 mph in still water. The boat is travelling in flowing water with a current velocity given by  . In what direction should the boat head to travel due east? (Represent the direction with a unit vector.)
A) i
B) 
C) 
D) The boat cannot travel due east against this current.

Accepted Answer

The answer of The motor of a small boat produces...

Question 7

Compute a + b. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Compute a + b. 
A) 
B) 
C)...

Question 8

Determine whether the vectors a and b are parallel. 
A) parallel
B) not parallel

Accepted Answer

Without knowing the values of the vectors a and b, we cannot determine if they are parallel or not. However, if we assume that they are not parallel, then the answer would be B because non-parallel vectors intersect at some angle.

Question 9

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

Accepted Answer

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

Question 10

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 
A) 
B) 
C) 
D)

Accepted Answer

To find the unit vector in the same direction as the given vector, we need to divide the vector by its magnitude. The magnitude of the given vector can be found using the Pythagorean theorem:
magnitude = sqrt[(287a - cdba)^2 + (84bc - 0168)^2 + (b77931ea8267 - 11eaa948)^2]
Once the magnitude is found, we divide each component of the vector by the magnitude to get the corresponding component of the unit vector. The resulting unit vector will have the same direction as the given vector, but with a magnitude of 1. Out of the given choices, only option C satisfies these conditions.

Question 11

Illustrate the sum a + b graphically. a = -2i - j; b = -3i + 2j 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Illustrate the sum a + b graphically....

Question 12

Find the distance between the given points. (0, -3, -1), (3, 6, 8)
A) 
B) 171
C) 
D) 67

Accepted Answer

The answer of Find the distance between the given points....

Question 13

Find a unit vector in the same direction as the given vector. -2i + 5j
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find a unit vector in the same...

Question 14

Find two unit vectors parallel to the given vector. 
A)  
B)  
C)  
D)

Accepted Answer

The answer of Find two unit vectors parallel to the...

Question 15

Find the vector with the given polar form. 
A) 
B) 
C) 
D)

Accepted Answer

In polar form, the vector is represented as magnitude times exponential of the angle, where the angle is in radians. Here, the magnitude is 11 and the angle is eaa948_cdb7_de5e_84bc_0f7edea93891_TB2342_11 in radians. The correct answer is therefore 11eaa948_cdb7_de5e_84bc_0f7edea93891_TB2342_11.

Question 16

Compute ||-2a - 4b||. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Compute ||-2a - 4b||. 
A) 
B) 
C)...

Question 17

Find a vector with the given magnitude in the same direction as the given vector. magnitude 2, v = 5i - j
A) 10i - 2j
B) 
C) 
D) 2i

Accepted Answer

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

Question 18

Compute 3a + 5b. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Compute 3a + 5b. 
A) 
B) 
C)...

Question 19

Determine whether the vectors a and b are parallel. 
A) parallel
B) not parallel

Accepted Answer

To determine if two vectors are parallel, we need to check if one vector is a scalar multiple of the other vector. 
If we have vectors a and b, then they are parallel if there is some scalar k such that a = kb. 
Without information about vectors a and b, it is impossible to say for certain if they are parallel or not.

Question 20

Suppose that there are two forces acting on a barge being towed along a river. One force is exerted due south by the river current and has a magnitude of 7 units (the exact nature of the force unit is unimportant). The other force is exerted by a tugboat and has a magnitude of 11 units towards the north and 3 units towards the east. What is the net force acting on the barge?
A) 11 units towards the north, 4 units towards the east
B) 18 units towards the north, 3 units towards the east
C) 4 units towards the north, 3 units towards the east
D) 3 units towards the north, 4 units towards the east

Accepted Answer

The net force towards the north is the difference between the force exerted by the tugboat (11 units north) and the river current (7 units south), resulting in 4 units towards the north. The eastward force remains unchanged at 3 units, as there is no opposing force in that direction.

Quiz 11: Vectors and the Geometry of Space

Illustrate the difference a - b graphically. a = -i + 4j; b = -3i + 3j

Find the vector with initial point A and terminal point B. A = (4, 2) , B = (-3, -7)

Find two unit vectors parallel to the given vector. From to

Compute -a - 2b.

The motor of a small boat produces a speed of 3 mph in still water. The boat is travelling in flowing water with a current velocity given by . In what direction should the boat head to travel due east? (Represent the direction with a unit vector.)

Compute a + b.

Determine whether the vectors a and b are parallel.

Compute ||2a - 3b||.

Illustrate the sum a + b graphically. a = -2i - j; b = -3i + 2j

Find the distance between the given points. (0, -3, -1) , (3, 6, 8)

Find a unit vector in the same direction as the given vector. -2i + 5j

Find two unit vectors parallel to the given vector.

Find the vector with the given polar form.

Compute ||-2a - 4b||.

Find a vector with the given magnitude in the same direction as the given vector. magnitude 2, v = 5i - j

Compute 3a + 5b.

Determine whether the vectors a and b are parallel.