We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 3 : Vector Subtraction

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 #282 : Vectors And Vector Operations

Find the difference u-v

u=<2,3>

v=<0,1>

Possible Answers:

<-2,-2>

<2,4>

<2,2>

Correct answer:

<2,2>

Explanation:

The difference a-b of two vectors <a_1,a_2> and <b_1,b_2> is defined as

<a_1-b_1,a_2-b_2>

For the two vectors

u=<2,3>

v=<0,1>

The difference is

u-v=<2,3>-<0,1>

=<2-0,3-1>

=<2,2>

Report an Error

Example Question #282 : Vectors And Vector Operations

Given the vectors

v=(1,3)

w=(5,2)

find v-w .

Possible Answers:

v-w=(6,5)

v-w=(4,-1)

v-w=(-4,1)

v-w=(1,-4)

Correct answer:

v-w=(-4,1)

Explanation:

Given the vectors

v=(1,3)

w=(5,2)

we can find the difference v-w by subtracting component-wise

v-w=(1,3)-(5,2)=(1-5,3-2)=(-4,1)

Report an Error

Example Question #3 : Vector Subtraction

Perform the following operation on the vectors specified below:

$3\mathbf{u}-2\mathbf{v}$

Where

$\mathbf{u}=4 \mathbf{i}+8\mathbf{j}+12\mathbf{k},\: \mathbf{v}=3\mathbf{i}+6\mathbf{j}+9\mathbf{k}$

Possible Answers:

$6\mathbf{i}+12\mathbf{j}+18\mathbf{k}$

$17\mathbf{i}+34\mathbf{j}+51\mathbf{k}$

$7\mathbf{i}+12\mathbf{j}+17\mathbf{k}$

$\mathbf{i}+2\mathbf{j}+3\mathbf{k}$

$18\mathbf{i}+36\mathbf{j}+54\mathbf{k}$

Correct answer:

$6\mathbf{i}+12\mathbf{j}+18\mathbf{k}$

Explanation:

First, multiply out the vectors by their corresponding coefficients:

$3\mathbf{u}=3(4\mathbf{i}+8\mathbf{j}+12\mathbf{k})=12\mathbf{i}+24\mathbf{j}+36\mathbf{k}$

$2\mathbf{v}=2(3\mathbf{i}+6\mathbf{j}+9\mathbf{k})=6\mathbf{i}+12\mathbf{j}+18\mathbf{k}$

Now we simply subtract the two vectors:

$3\mathbf{u}-2\mathbf{v}=(12-6)\mathbf{i}+(24-12)\mathbf{j}+(36-18)\mathbf{k}=6\mathbf{i}+12\mathbf{j}+18\mathbf{k}$

Report an Error

Example Question #3 : Vector Subtraction

Subtract the vectors $\left \langle -3,6,-9\right \rangle$ and $\left \langle -1,2,-9\right \rangle$ .

Possible Answers:

$\left \langle -2,4,0\right \rangle$

$\left \langle -2,0,4\right \rangle$

$\left \langle -2,4,-18\right \rangle$

$\left \langle -4,8,-18\right \rangle$

$\left \langle -4,4,-18\right \rangle$

Correct answer:

$\left \langle -2,4,0\right \rangle$

Explanation:

Set up an expression to subtract the vectors.

$\left \langle -3,6,-9\right \rangle-\left \langle -1,2,-9\right \rangle$

Be sure to make note of the sign change when subtracting the vectors.

$\left \langle -3-(-1),6-2,(-9)-(-9)\right \rangle$

Simplify the vector.

The answer is: $\left \langle -2,4,0\right \rangle$

Report an Error

Example Question #5 : Vector Subtraction

Find the difference, u-v , of the two vectors.
u=<-3,-7>
v=<6,4>

Possible Answers:

<-9,-11>

<3,-3>

<-3,3>

<9,11>

Correct answer:

<-9,-11>

Explanation:

To find the difference, u-v , we distribute the minus sign and turn it into vector addition.
u-v=<-3,-7>-<6,4>=<-3,-7>+<-6,-4>
The sum of two vectors is defined as

The sum of two vectors

a=<a_1, a_2>

b=<b_1, b_2>

is defined as

a+b=<a_1+b_1, a_2+b_2>

As such, the difference is

<-9,-11>

Report an Error

Example Question #1 : Vector Subtraction

Compute the following: $\left \langle 1,3,2\right \rangle-\left \langle 2,-4,1\right \rangle$ .

Possible Answers:

$\left \langle 3,-7,2\right \rangle$

$\left \langle -1,7,1\right \rangle$

$\left \langle -1,1,1\right \rangle$

$\left \langle -2,0,1\right \rangle$

Correct answer:

$\left \langle -1,7,1\right \rangle$

Explanation:

The formula for subtracting vectors is $a-b=\left \langle a_1-b_!,a_2-b_2,a_3-b_3\right \rangle$ . Plugging in the values we were given, we get $\left \langle (1-2),(3--4),(2-1)\right \rangle=\left \langle -1,7,1\right \rangle$

Report an Error

Example Question #2 : Vector Subtraction

Solve:

$\left \langle z, x, y^2z\right \rangle-\left \langle \ln(z), x, 2\right \rangle$

Possible Answers:

$\left \langle z-\ln(z), 1, y^2z-2\right \rangle$

$\left \langle z-\ln(z), 0, y^2z-2\right \rangle$

$z-\ln(z)+y^2z-2$

$\left \langle z, 2x, y^2z-2\right \rangle$

Correct answer:

$\left \langle z-\ln(z), 0, y^2z-2\right \rangle$

Explanation:

To subtract vectors, we simply subtract their respective components:

$\left \langle z-\ln(z), 0, y^2z-2\right \rangle$

Note that our result is a vector still.

Report an Error

Example Question #293 : Vectors And Vector Operations

Find the difference between $\left \langle 2,0,6\right \rangle$ and $\left \langle 3,3,1\right \rangle$ .

Possible Answers:

$\left \langle 2,0,5\right \rangle$

$\left \langle 0,-1,4\right \rangle$

$\left \langle -1,-3,5\right \rangle$

$\left \langle 1,3,1\right \rangle$

Correct answer:

$\left \langle -1,-3,5\right \rangle$

Explanation:

The formula for the difference of vectors is

$\left \langle x_1,x_2,x_3\right \rangle-\left \langle y_1,y_2,y_3\right \rangle=\left \langle x_1-y_1,x_2-y_2,x_3-y_3\right \rangle$

Using the vectors given, we get

$\left \langle 2-3,0-3,6-1\right \rangle=\left \langle -1,-3,5\right \rangle$ .

Report an Error

Example Question #3 : Vector Subtraction

Compute the following operation: $\left \langle 2,5,19\right \rangle-\left \langle 3,0,1\right \rangle$ .

Possible Answers:

$\left \langle 17,38,12\right \rangle$

$\left \langle 2,0,0\right \rangle$

$\left \langle -2,6,10\right \rangle$

$\left \langle -1,5,18\right \rangle$

Correct answer:

$\left \langle -1,5,18\right \rangle$

Explanation:

The formula for subtracting vectors a and b is

$a-b=\left \langle a_1-b_1,a_2-b_2,a_3-b_3\right \rangle$ .

Plugging in the values we were given, we get

$\left \langle (2-3),(5-0),(19-1)\right \rangle=\left \langle -1,5,18\right \rangle$

Report an Error

Example Question #4 : Vector Subtraction

Perform the following vector operation: $\left \langle 2,12,13\right \rangle-\left \langle 5,5,1\right \rangle$

Possible Answers:

$\left \langle 3,7,12\right \rangle$

$\left \langle -2,1,5\right \rangle$

$\left \langle -3,7,12\right \rangle$

Correct answer:

$\left \langle -3,7,12\right \rangle$

Explanation:

The formula for the difference of vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ is $a-b=\left \langle (x_1-x_2),(y_1-y_2),(z_1-z_2) \right \rangle$ . Using the vectors from the problem statement, we get $\left \langle (2-5),(12-5),(13-1) \right \rangle=\left \langle -3,7,12\right \rangle$

Report an Error

View Calculus 3 Tutors

Philipp
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mechanical Engineering.

View Calculus 3 Tutors

Bobby
Certified Tutor

University of Houston - Downtown, Bachelor of Science, Applied Mathematics.

View Calculus 3 Tutors

Dossevi
Certified Tutor

cole Ste Genevive Versailles, Bachelor of Science, Mathematics. Institut National Polytechnique de Grenoble, Master of Scienc...

All Calculus 3 Resources

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

Popular Subjects

Physics Tutors in San Francisco-Bay Area, French Tutors in San Diego, ACT Tutors in Washington DC, ISEE Tutors in Los Angeles, SAT Tutors in Seattle, GMAT Tutors in Denver, Computer Science Tutors in Boston, ISEE Tutors in San Diego, English Tutors in Dallas Fort Worth, GMAT Tutors in Chicago

Popular Courses & Classes

GMAT Courses & Classes in Denver, GRE Courses & Classes in Chicago, ACT Courses & Classes in Washington DC, ACT Courses & Classes in San Diego, SSAT Courses & Classes in New York City, SSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Philadelphia, GMAT Courses & Classes in San Diego, LSAT Courses & Classes in Chicago

Popular Test Prep

ISEE Test Prep in San Diego, ACT Test Prep in Boston, ACT Test Prep in Denver, LSAT Test Prep in Denver, SAT Test Prep in Chicago, SAT Test Prep in Philadelphia, ISEE Test Prep in Chicago, SSAT Test Prep in Phoenix, GMAT Test Prep in Washington DC, GRE Test Prep in Boston

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 : Vector Subtraction

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #282 : Vectors And Vector Operations

Example Question #282 : Vectors And Vector Operations

Example Question #3 : Vector Subtraction

Example Question #3 : Vector Subtraction

Example Question #5 : Vector Subtraction

Example Question #1 : Vector Subtraction

Example Question #2 : Vector Subtraction

Example Question #293 : Vectors And Vector Operations

Example Question #3 : Vector Subtraction

Example Question #4 : Vector Subtraction

All Calculus 3 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: