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:

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

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

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

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

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:

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

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

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

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

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:

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

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

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

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

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

Siddharth
Certified Tutor

University of Petroleum and Energy Studies and, Masters in Business Administration, Aviation Management.

View Calculus 3 Tutors

Kurosh
Certified Tutor

University of tehran, Bachelor of Engineering, Electrical Engineering.

View Calculus 3 Tutors

Jeremy
Certified Tutor

University of Illinois at Chicago, Bachelor of Science, Physics.

All Calculus 3 Resources

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

Popular Subjects

SSAT Tutors in New York City, Statistics Tutors in Boston, Spanish Tutors in Seattle, GRE Tutors in Philadelphia, English Tutors in Washington DC, Biology Tutors in Miami, Computer Science Tutors in San Diego, SSAT Tutors in Houston, MCAT Tutors in Seattle, ACT Tutors in Chicago

Popular Courses & Classes

SAT Courses & Classes in Boston, SAT Courses & Classes in Atlanta, SSAT Courses & Classes in Washington DC, MCAT Courses & Classes in Denver, GRE Courses & Classes in Washington DC, MCAT Courses & Classes in New York City, SSAT Courses & Classes in Chicago, LSAT Courses & Classes in Seattle, ISEE Courses & Classes in Philadelphia, SAT Courses & Classes in Houston

Popular Test Prep

GRE Test Prep in Seattle, GMAT Test Prep in Chicago, LSAT Test Prep in Chicago, GRE Test Prep in Miami, SSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Phoenix, SAT Test Prep in Los Angeles, ISEE Test Prep in Phoenix, LSAT Test Prep in Houston, GRE Test Prep in Houston

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: