We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 3 : Vectors and Vector Operations

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 #51 : Vector Addition

Find the sum of the vectors $\left \langle -3,-9,1\right \rangle$ and $\left \langle 15,10,4\right \rangle$

Possible Answers:

$\left \langle 11,1,5\right \rangle$

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

$\left \langle 12,1,5\right \rangle$

$\left \langle 1,4,5\right \rangle$

Correct answer:

$\left \langle 12,1,5\right \rangle$

Explanation:

To find the sum between vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the following formula:

$a+b=\left \langle(x_1+x_2),(y_1+y_2),(z_1+z_2) \right \rangle$

Using the vectors from the problem statement, we get

$\left \langle (-3+15),(-9+10),(1+4) \right \rangle=\left \langle 12,1,5\right \rangle$

Report an Error

Example Question #52 : Vector Addition

Find the sum of the vectors $\left \langle -9,-5,3\right \rangle$ and $\left \langle 2,0,-8\right \rangle$

Possible Answers:

$\left \langle -7,5,-5\right \rangle$

$\left \langle 6,-5,-5\right \rangle$

$\left \langle -7,-5,7\right \rangle$

$\left \langle -7,-5,-5\right \rangle$

Correct answer:

$\left \langle -7,-5,-5\right \rangle$

Explanation:

To find the sum of two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the following formula:

$a+b=\left \langle (x_1+x_2),(y_1+y_2),(z_1+z_2) \right \rangle$

Applying to the vectors from the problem statement, we get

$\left \langle -9+2,-5+0,3-8\right \rangle=\left \langle -7,-5,-5\right \rangle$

Report an Error

Example Question #53 : Vector Addition

Find the sum of the vectors $\left \langle -10,-13,15\right \rangle$ and $\left \langle 5,2,-9\right \rangle$

Possible Answers:

$\left \langle -5,-11,4\right \rangle$

$\left \langle -5,-11,6\right \rangle$

$\left \langle -5,-1,6\right \rangle$

$\left \langle 5,-11,6\right \rangle$

Correct answer:

$\left \langle -5,-11,6\right \rangle$

Explanation:

To find the sum of two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the following formula:

$a+b=\left \langle (x_1+x_2),(y_1+y_2),(z_1+z_2) \right \rangle$

Applying to the vectors from the problem statement, we get

$\left \langle -10+5,-13+2,15-9\right \rangle=\left \langle -5,-11,6\right \rangle$

Report an Error

Example Question #51 : Vector Addition

Find the sum of the vectors $\left \langle 3,-2,1\right \rangle$ , $\left \langle 9,0,2\right \rangle$ , and $\left \langle 1,0,1\right \rangle$

Possible Answers:

$\left \langle 12,-2,4\right \rangle$

$\left \langle 13,-4,4\right \rangle$

$\left \langle 13,-2,6\right \rangle$

$\left \langle 13,-2,4\right \rangle$

Correct answer:

$\left \langle 13,-2,4\right \rangle$

Explanation:

To find the sum of three vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ , $b=\left \langle x_2,y_2,z_2\right \rangle$ , and $c=\left \langle x_3,y_3,z_3\right \rangle$ , we use the following formula:

$a+b+c=\left \langle (x_1+x_2+x_3),(y_1+y_2+y_3),(z_1+z_2+z_3) \right \rangle$

Using the two vectors from the problem statement and applying, we get

$\left \langle (3+9+1),(-2+0+0),(1+2+1) \right \rangle=\left \langle 13,-2,4\right \rangle$

Report an Error

Example Question #54 : Vector Addition

Find the sum of the vectors $\left \langle 3,-8,-13\right \rangle$ and $\left \langle 4,0,7\right \rangle$

Possible Answers:

$\left \langle 3,5,-8\right \rangle$

$\left \langle 7,6,-8\right \rangle$

$\left \langle 7,8,-8\right \rangle$

$\left \langle 7,-8,-6\right \rangle$

Correct answer:

$\left \langle 7,-8,-6\right \rangle$

Explanation:

To find the sum of two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the following formula:

$a+b=\left \langle (x_1+x_2),(y_1+y_2),(z_1+z_2) \right \rangle$

Using the two vectors from the problem statement and applying, we get

$\left \langle (3+4),(-8+0),(-13+7) \right \rangle=\left \langle 7,-8,-6\right \rangle$

Report an Error

Example Question #55 : Vector Addition

Find the sum of the vectors $\left \langle 5,-18,3\right \rangle$ and $\left \langle 3,-6,5\right \rangle$

Possible Answers:

$\left \langle 6,-24,8\right \rangle$

$\left \langle 8,-14,8\right \rangle$

$\left \langle 8,10,20\right \rangle$

$\left \langle 8,-24,8\right \rangle$

Correct answer:

$\left \langle 8,-24,8\right \rangle$

Explanation:

To find the sum of two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we apply the following formula:
$a+b=\left \langle x_1+x_2,y_1+y_2,z_1+z_2\right \rangle$

Using the vectors from the problem statement, we get

$\left \langle 5+3,-18-6,3+5\right \rangle=\left \langle 8,-24,8\right \rangle$

Report an Error

Example Question #56 : Vector Addition

Find the sum of the vectors $\left \langle 7,-10,4\right \rangle$ and $\left \langle 2,-6,9\right \rangle$

Possible Answers:

$\left \langle 8,-16,13\right \rangle$

$\left \langle 9,-16,11\right \rangle$

$\left \langle 9,-9,13\right \rangle$

$\left \langle 9,-16,13\right \rangle$

Correct answer:

$\left \langle 9,-16,13\right \rangle$

Explanation:

Using the vectors from the problem statement, we get

$\left \langle 7+2,-10-6,4+9\right \rangle=\left \langle 9,-16,13\right \rangle$

Report an Error

Example Question #61 : Vector Addition

Find the sum of the vectors $\left \langle 2x,7y,z\right \rangle$ and $\left \langle 4x,4y,2z\right \rangle$

Possible Answers:

$\left \langle 6x,10y,3z\right \rangle$

$\left \langle 6x,11y,4\right \rangle$

$\left \langle 6x,11y,3z\right \rangle$

$\left \langle 5x,11y,3z\right \rangle$

Correct answer:

$\left \langle 6x,11y,3z\right \rangle$

Explanation:

To find the sum of two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the following formula:

$a+b=\left \langle (x_1+x_2),(y_1+y_2),(z_1+z_2) \right \rangle$

Applying to the vectors from the problem statement, we get

$\left \langle (2x+4x),(7y+4y),(z+2z) \right \rangle=\left \langle 6x,11y,3z\right \rangle$

Report an Error

Example Question #62 : Vector Addition

Find the sum of the vectors $\left \langle x,8y,3z\right \rangle$ and $\left \langle x,4y,5z\right \rangle$

Possible Answers:

$\left \langle 2x,10y,8z\right \rangle$

$\left \langle 2x,12y,8z\right \rangle$

$\left \langle 2x,2y,8z\right \rangle$

$\left \langle 2x,12y,9z\right \rangle$

Correct answer:

$\left \langle 2x,12y,8z\right \rangle$

Explanation:

To find the sum of two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , we use the following formula:

$a+b=\left \langle (x_1+x_2),(y_1+y_2),(z_1+z_2) \right \rangle$

Applying to the vectors from the problem statement, we get

$\left \langle (x+x),(8y+4y),(3z+5z) \right \rangle=\left \langle 2x,12y,8z\right \rangle$

Report an Error

Example Question #63 : Vector Addition

Find the sum of the vectors $\left \langle 2x,5y,z\right \rangle$ and $\left \langle 10x,9y,4z\right \rangle$

Possible Answers:

$\left \langle 12x,14y,5z\right \rangle$

$\left \langle 12x,10y,6z\right \rangle$

$\left \langle 2x,11y,8z\right \rangle$

$\left \langle 11x,14y,5z\right \rangle$

Correct answer:

$\left \langle 12x,14y,5z\right \rangle$

Explanation:

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

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

Using the vectors from the problem statement, we get

$\left \langle 2x+10x,5y+9y,z+4z\right \rangle=\left \langle 12x,14y,5z\right \rangle$

Report an Error

View Calculus 3 Tutors

George
Certified Tutor

Pensacola State College, Bachelor in Arts, Mathematics.

View Calculus 3 Tutors

Colton
Certified Tutor

Texas State University-San Marcos, Bachelor of Science, Mathematics.

View Calculus 3 Tutors

Pankaj
Certified Tutor

University of Delhi, Electrical Engineer, Electrical Engineering. Columbia University in the City of New York, Master of Arts...

All Calculus 3 Resources

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

Popular Subjects

French Tutors in Philadelphia, MCAT Tutors in Washington DC, GMAT Tutors in Miami, SSAT Tutors in Atlanta, SSAT Tutors in Houston, GMAT Tutors in Atlanta, SAT Tutors in Atlanta, Spanish Tutors in Philadelphia, Biology Tutors in San Francisco-Bay Area, Physics Tutors in Philadelphia

Popular Courses & Classes

GRE Courses & Classes in Houston, GRE Courses & Classes in Los Angeles, ISEE Courses & Classes in Phoenix, SSAT Courses & Classes in Seattle, GRE Courses & Classes in Atlanta, ACT Courses & Classes in San Diego, ACT Courses & Classes in Miami, GMAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Boston, ISEE Courses & Classes in Philadelphia

Popular Test Prep

MCAT Test Prep in Houston, GMAT Test Prep in Dallas Fort Worth, SAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in New York City, SSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Seattle, GRE Test Prep in Los Angeles, ACT Test Prep in Los Angeles, MCAT Test Prep in Washington DC, LSAT Test Prep in San Francisco-Bay Area

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 : Vectors and Vector Operations

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #51 : Vector Addition

Example Question #52 : Vector Addition

Example Question #53 : Vector Addition

Example Question #51 : Vector Addition

Example Question #54 : Vector Addition

Example Question #55 : Vector Addition

Example Question #56 : Vector Addition

Example Question #61 : Vector Addition

Example Question #62 : Vector Addition

Example Question #63 : Vector Addition

All Calculus 3 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: