We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 3 : Distance between Vectors

Study concepts, example questions & explanations for Calculus 3

Create An Account

All Calculus 3 Resources

6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : Distance Between Vectors

$\begin{align*}&\text{Find the distance between the two vectors:}\\&\overrightarrow{u}=\begin{bmatrix}8\\1\\-2\end{bmatrix}\overrightarrow{v}=\begin{bmatrix}-3\\10\\-16\end{bmatrix}\end{align*}$

Possible Answers:

16.00

19.95

21.68

4.00

Correct answer:

19.95

Explanation:

$\begin{align*}&\text{The distance between two vectors, }\overrightarrow{u}\text{ and }\overrightarrow{v}\text{ is found}\\&\text{by summing the squares of the distances between paired coordinates and}\\&\text{taking the square root of this sum:}\\&\sqrt{\sum_{i=1}^{n}(\overrightarrow{u}_{i}-\overrightarrow{v}_{i})^2}\\&\text{It is similar to finding the diagonal length of a rectangle or rectangular prism.}\\&\text{For our vectors }\begin{bmatrix}8\\1\\-2\end{bmatrix}\text{ and }\begin{bmatrix}-3\\10\\-16\end{bmatrix}\text{ this becomes:}\\&\sqrt{[8-(-3)]^2+[1-(10)]^2+[-2-(-16)]^2}\\&\sqrt{(11)^2+(-9)^2+(14)^2}\\&19.95\end{align*}$

Report an Error

Example Question #42 : Distance Between Vectors

$\begin{align*}&\text{Find the distance between the two vectors:}\\&\overrightarrow{u}=\begin{bmatrix}-18\\8\\0\end{bmatrix}\overrightarrow{v}=\begin{bmatrix}-2\\5\\-17\end{bmatrix}\end{align*}$

Possible Answers:

2.00

29.29

23.54

4.00

Correct answer:

23.54

Explanation:

$\begin{align*}&\text{The distance between two vectors, }\overrightarrow{u}\text{ and }\overrightarrow{v}\text{ is found}\\&\text{by summing the squares of the distances between paired coordinates and}\\&\text{taking the square root of this sum:}\\&\sqrt{\sum_{i=1}^{n}(\overrightarrow{u}_{i}-\overrightarrow{v}_{i})^2}\\&\text{It is similar to finding the diagonal length of a rectangle or rectangular prism.}\\&\text{For our vectors }\begin{bmatrix}-18\\8\\0\end{bmatrix}\text{ and }\begin{bmatrix}-2\\5\\-17\end{bmatrix}\text{ this becomes:}\\&\sqrt{[-18-(-2)]^2+[8-(5)]^2+[0-(-17)]^2}\\&\sqrt{(-16)^2+(3)^2+(17)^2}\\&23.54\end{align*}$

Report an Error

Example Question #43 : Distance Between Vectors

$\begin{align*}&\text{Calculate the distance between the two vectors:}\\&\begin{bmatrix}-1\\-20\\7\end{bmatrix}\text{ and }\begin{bmatrix}-13\\14\\6\end{bmatrix}\end{align*}$

Possible Answers:

36.07

21.00

20.02

4.58

Correct answer:

36.07

Explanation:

$\begin{align*}&\text{The distance between two vectors, }\overrightarrow{u}\text{ and }\overrightarrow{v}\text{ is found}\\&\text{by summing the squares of the distances between paired coordinates and}\\&\text{taking the square root of this sum:}\\&\sqrt{\sum_{i=1}^{n}(\overrightarrow{u}_{i}-\overrightarrow{v}_{i})^2}\\&\text{It is similar to finding the diagonal length of a rectangle or rectangular prism.}\\&\text{For our vectors }\begin{bmatrix}-1\\-20\\7\end{bmatrix}\text{ and }\begin{bmatrix}-13\\14\\6\end{bmatrix}\text{ this becomes:}\\&\sqrt{[-1-(-13)]^2+[-20-(14)]^2+[7-(6)]^2}\\&\sqrt{(12)^2+(-34)^2+(1)^2}\\&36.07\end{align*}$

Report an Error

Example Question #41 : Distance Between Vectors

Find the distance between the vectors $\left \langle 3,-3,-2\right \rangle$ and $\left \langle 1, 1, 7\right \rangle$

Possible Answers:

$\sqrt{111}$

$\sqrt{105}$

$\sqrt{101}$

Correct answer:

$\sqrt{101}$

Explanation:

To find the distance between two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , you use the formula:

$d=\sqrt{(a_1-b_1)^2+(a_2-b_2)^2+(a_3-b_3)^2}$

Using the vectors from the problem statement, we get

$d=\sqrt{(3-1)^2+(-3-1)^2+(-2-7)^2}=\sqrt{101}$

Report an Error

Example Question #45 : Distance Between Vectors

Find the distance between the vectors $\left \langle -5,-1,-3\right \rangle$ and $\left \langle 2, 6, -4\right \rangle$

Possible Answers:

$\sqrt{99}$

$\sqrt{103}$

$\sqrt{98}$

Correct answer:

$\sqrt{99}$

Explanation:

To find the distance between two vectors $a=\left \langle a_1,a_2,a_3\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , you use the formula:

$d=\sqrt{(a_1-b_1)^2+(a_2-b_2)^2+(a_3-b_3)^2}$

Using the vectors from the problem statement, we get

$d=\sqrt{(-5-2)^2+(-1-6)^2+(-3+4)^2}=\sqrt{99}$

Report an Error

View Calculus 3 Tutors

Dilip
Certified Tutor

University of Calcutta, Bachelor of Science, Physics. Indiana Institute of Technology, Master of Science, Physics.

View Calculus 3 Tutors

Jason
Certified Tutor

Brigham Young University, Bachelor, Neuroscience.

View Calculus 3 Tutors

Reza
Certified Tutor

University of Sherbrooke, Doctor of Philosophy, Mathematics. University of Manitoba, Master of Science, Mathematics.

All Calculus 3 Resources

6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in San Francisco-Bay Area, Math Tutors in New York City, Reading Tutors in Miami, LSAT Tutors in New York City, French Tutors in Atlanta, Physics Tutors in San Francisco-Bay Area, ISEE Tutors in Chicago, GMAT Tutors in San Diego, Calculus Tutors in Phoenix, Chemistry Tutors in Philadelphia

Popular Courses & Classes

LSAT Courses & Classes in Denver, GRE Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Chicago, ACT Courses & Classes in Chicago, GMAT Courses & Classes in Atlanta, Spanish Courses & Classes in Phoenix, SSAT Courses & Classes in Boston, GMAT Courses & Classes in Los Angeles, LSAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in New York City

Popular Test Prep

ACT Test Prep in New York City, LSAT Test Prep in Atlanta, MCAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in San Francisco-Bay Area, LSAT Test Prep in Chicago, SAT Test Prep in Seattle, GRE Test Prep in San Diego, GMAT Test Prep in Atlanta, GRE Test Prep in Philadelphia, MCAT Test Prep in Denver

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.

Please 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.

Please follow these steps 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)

* Please 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

Search 350+ Subjects

Calculus 3 : Distance between Vectors

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #41 : Distance Between Vectors

Example Question #42 : Distance Between Vectors

Example Question #43 : Distance Between Vectors

Example Question #41 : Distance Between Vectors

Example Question #45 : Distance Between Vectors

All Calculus 3 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: