Question 1

When vector   is added to vector   , which has a magnitude of 5.0, the vector representing their sum is perpendicular to   and has a magnitude that is twice that of   . What is the magnitude of   ?

Accepted Answer

A)  2.2 
B)  2.5 
C)  4.5 
D)  5.0 
E)  7.0 
A)  2.2 
B)  2.5 
C)  4.5 
D)  5.0 
E)  7.0

Question 2

If   = [15, 80°] and   , what is the magnitude of   ?

Accepted Answer

A)  15 
B)  35 
C)  32 
D)  5.0 
E)  23 
A)  15 
B)  35 
C)  32 
D)  5.0 
E)  23

Question 3

When three vectors,   ,   , and   are placed head to tail, the vector sum   . If the vectors all have the same magnitude, the angle between the directions of any two adjacent vectors is

Accepted Answer

A)  30° 
B)  60° 
C)  90° 
D)  120° 
E)  150° 
A)  30° 
B)  60° 
C)  90° 
D)  120° 
E)  150°

Question 4

A vector starts at coordinate (3.0, 4.0) and ends at coordinate (−2.0, 16.0). What are the magnitude and direction of this vector?

Accepted Answer

The answer of A vector starts at coordinate (3.0, 4.0)...

Question 5

If vector   is added to vector   , the result is   . If   is subtracted from   , the result is   . What is the direction of   (to the nearest degree)?

Accepted Answer

A)  225° 
B)  221° 
C)  230° 
D)  236° 
E)  206° 
A)  225° 
B)  221° 
C)  230° 
D)  236° 
E)  206°

Question 6

Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What distance separates the two oases?

Accepted Answer

A)  15 km 
B)  48 km 
C)  28 km 
D)  53 km 
E)  55 km 
A)  15 km 
B)  48 km 
C)  28 km 
D)  53 km 
E)  55 km

Question 7

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
Exhibit 3-3
The vectors   ,   , and   are shown below.   Use this exhibit to answer the following question(s).
-Refer to Exhibit 3-3. Which diagram below correctly represents   ?

Accepted Answer

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

Question 8

A vector,   , when added to the vector   yields a resultant vector which is in the positive y direction and has a magnitude equal to that of   . What is the magnitude of   ?

Accepted Answer

A)  3.2 
B)  6.3 
C)  9.5 
D)  18 
E)  5 
A)  3.2 
B)  6.3 
C)  9.5 
D)  18 
E)  5

Question 9

If   = [2.5 cm, 80°], i.e., the magnitude and direction of   are 2.5 cm and 80°,   = [3.5 cm, 120°], and   , what is the direction of   (to the nearest degree)?

Accepted Answer

A)  247° 
B)  235° 
C)  243° 
D)  216° 
E)  144° 
A)  247° 
B)  235° 
C)  243° 
D)  216° 
E)  144°

Question 10

Given that   and   , what is   ?

Accepted Answer

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

Question 11

In what quadrant are both the sine and tangent negative?

Accepted Answer

A)  1st 
B)  2nd 
C)  3rd 
D)  4th 
E)  This cannot happen. 
A)  1st 
B)  2nd 
C)  3rd 
D)  4th 
E)  This cannot happen.

Question 12

If   and   , what is the magnitude of the vector   ?

Accepted Answer

A)  42 
B)  22 
C)  64 
D)  90 
E)  13 
A)  42 
B)  22 
C)  64 
D)  90 
E)  13

Question 13

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
Exhibit 3-3
The vectors   ,   , and   are shown below.   Use this exhibit to answer the following question(s).
-Refer to Exhibit 3-4. The total displacement of the sailboat, the vector sum of its displacements OB, BC, CD and DE, is

Accepted Answer

A)  1732 m, East. 
B)  2000 m, Northeast. 
C)  6298 m, East. 
D)  8000 m, Southeast. 
E)  8000 m, East. 
A)  1732 m, East. 
B)  2000 m, Northeast. 
C)  6298 m, East. 
D)  8000 m, Southeast. 
E)  8000 m, East.

Question 14

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
Exhibit 3-1
The three forces shown act on a particle.   Use this exhibit to answer the following question(s).
-Refer to Exhibit 3-1. What is the magnitude of the resultant of these three forces?

Accepted Answer

A)  27.0 N 
B)  33.2 N 
C)  36.3 N 
D)  23.8 N 
E)  105 N 
A)  27.0 N 
B)  33.2 N 
C)  36.3 N 
D)  23.8 N 
E)  105 N

Question 15

Adding vectors   and   by the graphical method gives the same result for   +   and   +   . If both additions are done graphically from the same origin, the resultant is the vector that goes from the tail of the first vector to the tip of the second vector, i.e, it is represented by a diagonal of the parallelogram formed by showing both additions in the same figure. Note that a parallelogram has 2 diagonals. Keara says that the sum of two vectors by the parallelogram method is   . Shamu says it is   . Both used the parallelogram method, but one used the wrong diagonal. Which one of the vector pairs below contains the original two vectors?

Accepted Answer

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

Question 16

If   and   , what is the direction of the vector   ?

Accepted Answer

A)  −49° 
B)  −41° 
C)  −90° 
D)  +49° 
E)  +21° 
A)  −49° 
B)  −41° 
C)  −90° 
D)  +49° 
E)  +21°

Question 17

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
-A student decides to spend spring break by driving 50 miles due east, then 50 miles 30 degrees south of east, then 50 miles 30 degrees south of that direction, and to continue to drive 50 miles deviating by 30 degrees each time until he returns to his original position. How far will he drive, and how many vectors must he sum to calculate his displacement?

Accepted Answer

A)  0, 0 
B)  0, 8 
C)  0, 12 
D)  400 mi, 8 
E)  600 mi, 12 
A)  0, 0 
B)  0, 8 
C)  0, 12 
D)  400 mi, 8 
E)  600 mi, 12

Question 18

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
Exhibit 3-3
The vectors   ,   , and   are shown below.   Use this exhibit to answer the following question(s).
-Refer to Exhibit 3-4. The total distance it travels is

Accepted Answer

A)  1000 m. 
B)  1732 m. 
C)  2000 m. 
D)  6298 m. 
E)  8000 m. 
A)  1000 m. 
B)  1732 m. 
C)  2000 m. 
D)  6298 m. 
E)  8000 m.

Question 19

Given two non-zero vectors,   and   , such that   , the sum   satisfies

Accepted Answer

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

Question 20

If   = [10 m, 30°] and   = [25 m, 130°], what is the magnitude of the sum of these two vectors?

Accepted Answer

A)  20 m 
B)  35 m 
C)  15 m 
D)  25 m 
E)  50 m 
A)  20 m 
B)  35 m 
C)  15 m 
D)  25 m 
E)  50 m

Exam 3: Vectors

When vector is added to vector , which has a magnitude of 5.0, the vector representing their sum is perpendicular to and has a magnitude that is twice that of . What is the magnitude of ?

If = [15, 80°] and , what is the magnitude of ?

When three vectors, , , and are placed head to tail, the vector sum . If the vectors all have the same magnitude, the angle between the directions of any two adjacent vectors is

A vector starts at coordinate (3.0, 4.0) and ends at coordinate (−2.0, 16.0). What are the magnitude and direction of this vector?

If vector is added to vector , the result is . If is subtracted from , the result is . What is the direction of (to the nearest degree)?

Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What distance separates the two oases?

Instructions: On occasion, the notation = [A, θ] will be a shorthand notation for . Exhibit 3-3 The vectors , , and are shown below. Use this exhibit to answer the following question(s). -Refer to Exhibit 3-3. Which diagram below correctly represents ?

A vector, , when added to the vector yields a resultant vector which is in the positive y direction and has a magnitude equal to that of . What is the magnitude of ?

If = [2.5 cm, 80°], i.e., the magnitude and direction of are 2.5 cm and 80°, = [3.5 cm, 120°], and , what is the direction of (to the nearest degree)?

Given that and , what is ?

In what quadrant are both the sine and tangent negative?

If and , what is the magnitude of the vector ?

Instructions: On occasion, the notation = [A, θ] will be a shorthand notation for . Exhibit 3-1 The three forces shown act on a particle. Use this exhibit to answer the following question(s). -Refer to Exhibit 3-1. What is the magnitude of the resultant of these three forces?

If and , what is the direction of the vector ?

Instructions: On occasion, the notation = [A, θ] will be a shorthand notation for . Exhibit 3-3 The vectors , , and are shown below. Use this exhibit to answer the following question(s). -Refer to Exhibit 3-4. The total distance it travels is

Given two non-zero vectors, and , such that , the sum satisfies

If = [10 m, 30°] and = [25 m, 130°], what is the magnitude of the sum of these two vectors?

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