We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 3 : Dot Product

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 #141 : Dot Product

Find the dot product between the vectors $\left \langle 3,0,-6\right \rangle$ and $\left \langle 1,-2,3\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product between vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , you apply the following formula:

$a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$ . Applying to the vectors from the problem statement, we get:

(3*1)+(0*-2)+(-6*3)=-15

Report an Error

Example Question #142 : Dot Product

Find the dot product between the vectors $\left \langle x^3,3,1\right \rangle$ and $\left \langle 4x^3,-7,2\right \rangle$

Possible Answers:

x^4-16

3x^6-17

7x-10

4x^6-19

Correct answer:

4x^6-19

Explanation:

To find the dot product between vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $b=\left \langle x_2,y_2,z_2\right \rangle$ , you apply the following formula:

$a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$ . Applying to the vectors from the problem statement, we get:

(x^3*4x^3)+(3*-7)+(1*2)=4x^6-19

Report an Error

Example Question #141 : Dot Product

Find the dot product of the two vectors:

$\left \langle 3, xz, yz^2\right \rangle \cdot \left \langle xy, xyz, z\right \rangle$

Possible Answers:

3xy+xyz^2+yz^3

3xy+x^2yz^2+yz^3

3xy+x^2yz^2+yz

$\left \langle 3xy, x^2yz^2,yz^3 \right \rangle$

Correct answer:

3xy+x^2yz^2+yz^3

Explanation:

The dot product of two vectors is given by the sum of the products of the corresponding components (for example, $\left \langle a,b\right \rangle \cdot \left \langle c,d\right \rangle = ac+bd$ )

Our final answer is

3xy+x^2yz^2+yz^3

Report an Error

Example Question #142 : Dot Product

What is the product of $\vec {a}=<-2,0,7>$ and $\vec {b}=<-3,4,1>$

Possible Answers:

Correct answer:

Explanation:

Screen shot 2016 01 07 at 8.41.42 pm

Report an Error

Example Question #143 : Dot Product

Evaluate the dot product of the vectors <23, 78>,<42,64> .

Possible Answers:

$\approx 148.781$

5958

None of the other answers

200

573

Correct answer:

5958

Explanation:

To evaluate the dot product of any two vectors, we multiply them component-wise.

$23\times42 +78 \times 64 = 5958$ .

Report an Error

Example Question #144 : Dot Product

Solve:

$\left \langle \cos^2(z), 4\right \rangle\cdot \left \langle 4, \sin^2(z)\right \rangle$

Possible Answers:

$\left \langle 4\cos^2(z), 4\sin^2(z)\right \rangle$

$\left \langle 4\right \rangle$

Correct answer:

Explanation:

The dot product of two vectors is given by the sum of the products of their respective components (for example, $\left \langle a, b\right \rangle \cdot \left \langle c,d \right \rangle = ac+bd$ )

Our final answer is

$4(\cos^2(z)+\sin^2(z))=4$

Report an Error

Example Question #147 : Dot Product

Evaluate the dot product of the two vectors.

u=<1,4>

v=<-2,3>

Possible Answers:

Correct answer:

Explanation:

The dot product for the vectors

a=<a_1,a_2>

b=<b_1,b_2>

is defined as

$a\bullet b=a_1*b_1+a_2*b_2$

For the vectors in this problem we find that

$u\bullet v=1*(-2)+4(3)=-2+12=10$

Report an Error

Example Question #148 : Dot Product

Evaluate the dot product of the two vectors

u=<-2,-7>

v=<3,5>

Possible Answers:

210

Correct answer:

Explanation:

The dot product for the vectors

a=<a_1,a_2>

b=<b_1,b_2>

is defined as

$a\bullet b=a_1*b_1+a_2*b_2$

For the vectors in this problem we find that

$u\bullet v=-2*3+(-7)*5=-6-35=-41$

Report an Error

Example Question #149 : Dot Product

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

Possible Answers:

Correct answer:

Explanation:

To find the dot product between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $\left \langle x_2,y_2,z_2\right \rangle$ , we use the formula

$a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$

Using the vectors from the problem statement, we get

(5*4)+(2*-3)+(1*-6)=8

Report an Error

Example Question #150 : Dot Product

Find the dot product between the vectors $\left \langle 15,12,10\right \rangle$ and $\left \langle 1,3,2\right \rangle$

Possible Answers:

Correct answer:

Explanation:

To find the dot product between two vectors $a=\left \langle x_1,y_1,z_1\right \rangle$ and $\left \langle x_2,y_2,z_2\right \rangle$ , we use the formula

$a\cdot b=(x_1*x_2)+(y_1*y_2)+(z_1*z_2)$

Using the vectors from the problem statement, we get

(15*1)+(12*3)+(10*2)=71

Report an Error

View Calculus 3 Tutors

Sajad
Certified Tutor

Western University, Doctor of Science, Mathematics.

View Calculus 3 Tutors

Harriet
Certified Tutor

St. Olaf College, Bachelors, Math and Physics.

View Calculus 3 Tutors

Elvis
Certified Tutor

Methodist University, Bachelor of Science, Mathematics and Computer Science.

All Calculus 3 Resources

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

Popular Subjects

Computer Science Tutors in Los Angeles, ACT Tutors in San Diego, LSAT Tutors in New York City, Reading Tutors in Los Angeles, ACT Tutors in Chicago, Computer Science Tutors in Philadelphia, Spanish Tutors in San Francisco-Bay Area, Calculus Tutors in Philadelphia, ACT Tutors in Houston, GMAT Tutors in New York City

Popular Courses & Classes

LSAT Courses & Classes in Miami, GRE Courses & Classes in Seattle, GRE Courses & Classes in New York City, ISEE Courses & Classes in Phoenix, GRE Courses & Classes in Philadelphia, GRE Courses & Classes in Denver, SSAT Courses & Classes in Washington DC, SAT Courses & Classes in Miami, ACT Courses & Classes in Atlanta, SAT Courses & Classes in New York City

Popular Test Prep

MCAT Test Prep in San Diego, SAT Test Prep in New York City, ACT Test Prep in Denver, GMAT Test Prep in Boston, SSAT Test Prep in San Diego, ACT Test Prep in Houston, ACT Test Prep in Boston, MCAT Test Prep in Atlanta, ACT Test Prep in Dallas Fort Worth, SSAT Test Prep in Washington DC

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 : Dot Product

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #141 : Dot Product

Example Question #142 : Dot Product

Example Question #141 : Dot Product

Example Question #142 : Dot Product

Example Question #143 : Dot Product

Example Question #144 : Dot Product

Example Question #147 : Dot Product

Example Question #148 : Dot Product

Example Question #149 : Dot Product

Example Question #150 : Dot Product

All Calculus 3 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: