Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Vectors

Study concepts, example questions & explanations for Trigonometry

Create An Account Create Tests & Flashcards

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 :Vectors

Determine the magnitude of vector A.

Possible Answers:

$|\vec{A}| = 16$

$|\vec{A}| = 5$

$|\vec{A}| = 12$

$|\vec{A}| = 25$

Correct answer:

$|\vec{A}| = 5$

Explanation:

We can use the pythagorean theorem to solve this problem. Using $\vec{A}$ as our hypotenuse, we can drop a vertical vector perpendicular to the x-axis. We will call this $\vec{A_y}$ and it is 4 units in length. We can also extend a vector from the origin that connects to $\vec{A_y}$ . We will call this $\vec{A_x}$ and it is 3 units in length.

Using the pythagorean theorem:

$|\vec{A}|^2 = \vec{A_x}^2 + \vec{A_y}^2$

$|\vec{A}| = \sqrt{\vec{A_x}^2 + \vec{A_y}^2}$

$|\vec{A}| = \sqrt{3^2 + 4^2}$

$|\vec{A}| = \sqrt{9 + 16}$

$|\vec{A}| = \sqrt{25}$

$|\vec{A}| = 5$

Report an Error

Example Question #1 :Vectors

Which of the following is the correct term for the sum of two vectors?

Possible Answers:

Resultant

Sum

Velocity

Magnitude

Correct answer:

Resultant

Explanation:

When summing two vectors, you have both an x and y component and you sum these separately leaving you with a coordinate as your answer. This coordinate is called a resultant.

Report an Error

Example Question #3 :Vectors

Determine the resultant of $\vec{A} = (2,5)$ and $\vec{B} = (1,9)$ .

Possible Answers:

$\vec{A} + \vec{B} = (14, 3)$

$\vec{A} + \vec{B} = (3, 14)$

$\vec{A} + \vec{B} = (1, -4)$

$\vec{A} + \vec{B} = 17$

Correct answer:

$\vec{A} + \vec{B} = (3, 14)$

Explanation:

When determining the resultant of two vectors, you are finding the sum of two vectors. To do this you must add the x component and the y component separately.

$\vec{A}+\vec{B} = (2,5) + (1,9)$

$\vec{A}+\vec{B} = (2 + 1, 5 + 9)$

$\vec{A} + \vec{B} = (3, 14)$

Report an Error

Example Question #4 :Vectors

Consider the following graphs where $\vec{A}$ begins at the origin and ends at (-3, 5) and $\vec{B} = (4, 1)$ . Which of the following depicts the correct resultant of these two vectors.

Screen shot 2020 08 27 at 1.29.58 pm

Possible Answers:

Screen shot 2020 08 27 at 1.32.16 pm

Screen shot 2020 08 27 at 1.33.16 pm

Screen shot 2020 08 27 at 1.32.49 pm

Screen shot 2020 08 27 at 1.31.51 pm

Correct answer:

Screen shot 2020 08 27 at 1.33.16 pm

Explanation:

To find the resultant we must sum the two vectors:

$\vec{A} + \vec{B} = (-3, 5) + (4, 1)$

$\vec{A} + \vec{B} = (-3 + 4, 5 + 1)$

$\vec{A} + \vec{B} = (1, 6)$

Now we must graph the resultant

Screen shot 2020 08 27 at 1.31.14 pm

Report an Error

Example Question #5 :Vectors

How many degrees above the x-axis is $\vec{A}$ ?

Screen shot 2020 08 27 at 2.25.43 pm

Possible Answers:

23.2^o

66.8^o

43.7^o

113.2^o

Correct answer:

23.2^o

Explanation:

First, we must understand what we are solving for. We are solving for the angle that is formed by $\vec{A}$ 和轴。要做到这一点,我们可以扩展一个向量from the origin which stops directly under the end of $\vec{A}$ . We will call this new vector $\vec{A_x}$ and it will be 7 units long. We will also extend a vector upwards that is perpendicular to the x-axis. We will call this $\vec{A_y}$ and it will be 3 units long.

Screen shot 2020 08 27 at 2.26.24 pm

Now we can use the relationship that $tan(\theta) = \frac{opposite}{adjacent}$ where $\vec{A_x}$ is the adjacent side and $\vec{A_y}$ is the opposite side.

$tan(\theta) = \frac{\vec{A_y}}{\vec{A_x}}$

$tan(\theta) = \frac{3}{7}$

$\theta = tan_{-1}(\frac{3}{7})$

$\theta = 23.2$

And so $\vec{A}$ is 23.2 degrees above the x-axis.

Report an Error

Example Question #1 :Vectors

Find the difference of the two vectors, $\vec{A}$ which ends at (-2, 4) and $\vec{B}$ ending at (7, -6) .

Possible Answers:

(-9, 10)

Correct answer:

(-9, 10)

Explanation:

When finding the difference of two vectors, you must subtract the x and y components separately.

$\vec{A} - \vec{B} = (-2, 4) - (7, -6)$

$\vec{A} - \vec{B} = (-2-7, 4 - (-6))$

$\vec{A} - \vec{B} = (-9, 10)$

Report an Error

Example Question #1 :Vectors

Which of the following is the correct depiction of the difference of vectors A and B?

Screen shot 2020 08 27 at 1.42.05 pm

Possible Answers:

Screen shot 2020 08 27 at 1.43.44 pm

Screen shot 2020 08 27 at 1.43.01 pm

Screen shot 2020 08 27 at 1.43.50 pm

Screen shot 2020 08 27 at 1.43.37 pm

Correct answer:

Screen shot 2020 08 27 at 1.43.01 pm

Explanation:

To find the difference of two vectors we must consider the x and y components separately.

$\vec{A} - \vec{B} = (5, 8) - (-3, 10)$

$\vec{A} - \vec{B} = (5 - (-3), 8 - 10)$

$\vec{A} = \vec{B} = (8, -2)$

And then we must correctly graph this vector

Screen shot 2020 08 27 at 1.43.01 pm

Report an Error

Example Question #8 :Vectors

True or False: The magnitude of a vector is the length of the vector.

Possible Answers:

True

False

Correct answer:

True

Explanation:

When finding the magnitude of the vector, you use either the Pythagorean Theorem by forming a right triangle with the vector in question or you can use the distance formula. This is much more clear considering the distance vector that the magnitude of the vector is in fact the length of the vector.

Report an Error

View Trigonometry Tutors

Francisco
Certified Tutor

University of Texas at Brownsville, Bachelors, Mathematics. University of Texas at Brownsville, Masters, Mathematics.

View Trigonometry Tutors

Bruce
Certified Tutor

Colorado School of Mines, Engineer, Chemical Engineering.

View Trigonometry Tutors

Luke
Certified Tutor

赫尔大学理学学士,算cs. University of Leeds, Master of Science, Mathematics.

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Trigonometry Tutoring in Top Cities:

Trigonometry Tutors in Top Cities:

Popular Courses & Classes

MCAT Courses & Classes in Los Angeles,LSAT Courses & Classes in Los Angeles,SAT Courses & Classes in Washington DC,GRE Courses & Classes in Washington DC,SSAT Courses & Classes in Miami,Spanish Courses & Classes in Houston,SAT Courses & Classes in Houston,GMAT Courses & Classes in New York City,GMAT Courses & Classes in Miami,SSAT Courses & Classes in Atlanta

Popular Test Prep

MCAT Test Prep in Chicago,SSAT Test Prep in Atlanta,SSAT Test Prep in New York City,MCAT Test Prep in Miami,MCAT Test Prep in Los Angeles,SAT Test Prep in Houston,SAT Test Prep in New York City,SAT Test Prep in Dallas Fort Worth,LSAT Test Prep in Dallas Fort Worth,SSAT Test Prep in Los Angeles

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

请求se be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

请按照以下步骤to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

*Full legal name

Company name

*Phone number

*Email address

Address

*Address1

Address2

*City

*State

*Zipcode

*Country

Complaint Details

*URL of copyrighted work (where your original material is located)

*请求se describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

*Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

搜索350 +主题

Trigonometry : Vectors

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 :Vectors

Example Question #1 :Vectors

Example Question #3 :Vectors

Example Question #4 :Vectors

Example Question #5 :Vectors

Example Question #1 :Vectors

Example Question #1 :Vectors

Example Question #8 :Vectors

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Find the Best Tutors

Email address:
Your name:
Feedback: