Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Vector Calculations

Study concepts, example questions & explanations for Calculus 2

Create An Account

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #51 : Vector Calculations

What is the cross product of $a=\left \langle -1,0,8\right \rangle$ and $b=\left \langle -8,-1, 0 \right \rangle$ ?

Possible Answers:

$\left \langle -8,-64, 1 \right \rangle$

$\left \langle -8,64, 1 \right \rangle$

$\left \langle 8,64, 1 \right \rangle$

$\left \langle -8,64, -1 \right \rangle$

$\left \langle -8,-64, -1 \right \rangle$

Correct answer:

$\left \langle 8,64, 1 \right \rangle$

Explanation:

In order to find the cross product of two three-dimensional vectors, we must find the determinant of a matrix comprised of the vectors' elements. That is, if $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ and $b=\left \langle b_{1},b_{2},b_{3}\right \rangle$ , then

$a\times b=\begin{Bmatrix} i&j &k \\ a_{1}&a_{2} &a_{3} \\ b_{1}&b_{2} &b_{3} \end{Bmatrix}=\left \langle a_{2}b_{3}-a_{3}b_{2}, a_{1}b_{3}-a_{3}b_{1},a_{1}b_{2}-a_{2}b_{1} \right \rangle$ .

Given $a=\left \langle -1,0,8\right \rangle$ and $b=\left \langle -8,-1, 0 \right \rangle$ , the cross product $a \times b$ is:

$\begin{Bmatrix} i&j &k \\ -1&0 &8 \\ -8&-1 &0 \end{Bmatrix}$

$=\left \langle (0)(0)-(8)(-1), (-1)(0)-(8)(-8), (-1)(-1)-(0)(-8) \right \rangle$

$=\left \langle 0+8, 0+64, 1-0 \right \rangle$

$=\left \langle 8,64, 1 \right \rangle$

Report an Error

Example Question #211 : Vector

What is the norm of $a=\left \langle 2,4,6\right \rangle$ ?

Possible Answers:

$2\sqrt{15}$

$2\sqrt{14}$

$3\sqrt{6}$

$3\sqrt{7}$

$\sqrt{55}$

Correct answer:

$2\sqrt{14}$

Explanation:

In order to find the norm of a vector, we must first find the sum of the squares of the vector's elements and take the square root of that sum. Given $a=\left \langle 2,4,6\right \rangle$ , then:

$\left \| a\right \|=\sqrt{(2)^{2}+(4)^{2}+(6)^{2}}$

$\left \| a\right \|=\sqrt{4+16+36}$

$\left \| a\right \|=\sqrt{20+36}$

$\left \| a\right \|=\sqrt{56}$

$\left \| a\right \|=\sqrt{4\times 14}$

$\left \| a\right \|=2\sqrt{14}$

Report an Error

Example Question #551 : Parametric, Polar, And Vector

What is the norm of $a=\left \langle 3,5,7\right \rangle$ ?

Possible Answers:

$\sqrt{83}$

$3\sqrt{10}$

$3\sqrt{11}$

Correct answer:

$\sqrt{83}$

Explanation:

In order to find the norm of a vector, we must first find the sum of the squares of the vector's elements and take the square root of that sum. Given $a=\left \langle 3,5,7\right \rangle$ , then:

$\left \| a\right \|=\sqrt{(3)^{2}+(5)^{2}+(7)^{2}}$

$\left \| a\right \|=\sqrt{9+25+49}$

$\left \| a\right \|=\sqrt{34+49}$

$\left \| a\right \|=\sqrt{83}$

Report an Error

Example Question #51 : Vector Calculations

What is the norm of $a=\left \langle9,3,6\right \rangle$ ?

Possible Answers:

$3\sqrt{14}$

$3\sqrt{11}$

$3\sqrt{10}$

$3\sqrt{13}$

Correct answer:

$3\sqrt{14}$

Explanation:

In order to find the norm of a vector, we must first find the sum of the squares of the vector's elements and take the square root of that sum. Given $a=\left \langle9,3,6\right \rangle$ , then:

$\left \| a\right \|=\sqrt{(9)^{2}+(3)^{2}+(6)^{2}}$

$\left \| a\right \|=\sqrt{81+9+36}$

$\left \| a\right \|=\sqrt{90+36}$

$\left \| a\right \|=\sqrt{126}$

$\left \| a\right \|=\sqrt{9\times 14}$

$\left \| a\right \|=3\sqrt{14}$

Report an Error

Example Question #1073 : Calculus Ii

Find the cross product of $a=\left \langle 5,7,2\right \rangle$ and $b=\left \langle 4,4,8\right \rangle$ .

Possible Answers:

None of the above

$\left \langle 48, 32, -8\right \rangle$

$\left \langle 20, 32, 8\right \rangle$

$\left \langle -20, -32, -8\right \rangle$

$\left \langle 20, -32, -8\right \rangle$

Correct answer:

$\left \langle 48, 32, -8\right \rangle$

Explanation:

$a\times b=\begin{Bmatrix} i&j &k \\ a_{1}&a_{2} &a_{3} \\ b_{1}&b_{2} &b_{3} \end{Bmatrix}=\left \langle a_{2}b_{3}-a_{3}b_{2}, a_{1}b_{3}-a_{3}b_{1},a_{1}b_{2}-a_{2}b_{1} \right \rangle$ .

Given $a=\left \langle 5,7,2\right \rangle$ and $b=\left \langle 4,4,8\right \rangle$ . the cross product $a \times b$ is:

$\begin{Bmatrix} i&j &k \\ 5&7 &2 \\ 4&4 &8 \end{Bmatrix}$

$=\left \langle (7)(8)-(2)(4), (5)(8)-(2)(4), (5)(4)-(7)(4) \right \rangle$

$=\left \langle 56-8, 40-8, 20-28\right \rangle$

$=\left \langle 48, 32, -8\right \rangle$

Report an Error

Example Question #1074 : Calculus Ii

What is the cross product of $a=\left \langle 9,8,7\right \rangle$ and $b=\left \langle 0,1,2\right \rangle$ ?

Possible Answers:

$\left \langle -9, 18, 9 \right \rangle$

$\left \langle -9, -18, -9 \right \rangle$

$\left \langle -9, -18, 9 \right \rangle$

$\left \langle -9, 18, -9 \right \rangle$

$\left \langle 9, 18, 9 \right \rangle$

Correct answer:

$\left \langle 9, 18, 9 \right \rangle$

Explanation:

$a\times b=\begin{Bmatrix} i&j &k \\ a_{1}&a_{2} &a_{3} \\ b_{1}&b_{2} &b_{3} \end{Bmatrix}=\left \langle a_{2}b_{3}-a_{3}b_{2}, a_{1}b_{3}-a_{3}b_{1},a_{1}b_{2}-a_{2}b_{1} \right \rangle$ .

Given $a=\left \langle 9,8,7\right \rangle$ and $b=\left \langle 0,1,2\right \rangle$ , the cross product $a \times b$ is:

$\begin{Bmatrix} i&j &k \\ 9&8 &7 \\ 0&1 &2 \end{Bmatrix}$

$=\left \langle (8)(2)-(7)(1), (9)(2)-(7)(0), (9)(1)-(8)(0) \right \rangle$

$=\left \langle 16-7, 18-0, 9-0 \right \rangle$

$=\left \langle 9, 18, 9 \right \rangle$

Report an Error

Example Question #51 : Vector Calculations

What is the cross product of $a=\left \langle 7,-4,3\right \rangle$ and $b=\left \langle 5,-5,5\right \rangle$ ?

Possible Answers:

$\left \langle -5, 20, 15 \right \rangle$

$\left \langle -5,-20, -15 \right \rangle$

$\left \langle 5, 20, -15 \right \rangle$

$\left \langle 5, 20, 15 \right \rangle$

$\left \langle -5, 20, -15 \right \rangle$

Correct answer:

$\left \langle -5, 20, -15 \right \rangle$

Explanation:

$a\times b=\begin{Bmatrix} i&j &k \\ a_{1}&a_{2} &a_{3} \\ b_{1}&b_{2} &b_{3} \end{Bmatrix}=\left \langle a_{2}b_{3}-a_{3}b_{2}, a_{1}b_{3}-a_{3}b_{1},a_{1}b_{2}-a_{2}b_{1} \right \rangle$ .

Given $a=\left \langle 7,-4,3\right \rangle$ and $b=\left \langle 5,-5,5\right \rangle$ , the cross product $a \times b$ is:

$\begin{Bmatrix} i&j &k \\ 7&-4 &3 \\ 5&-5 &5 \end{Bmatrix}$

$=\left \langle (-4)(5)-(3)(-5), (7)(5)-(3)(5), (7)(-5)-(-4)(5) \right \rangle$

$=\left \langle -20+15, 35-15, -35+20 \right \rangle$

$=\left \langle -5, 20, -15 \right \rangle$

Report an Error

Example Question #1076 : Calculus Ii

What is the cross product of $a=\left \langle 0,-3,3\right \rangle$ and $b=\left \langle -3,0,3\right \rangle$ ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

$a\times b=\begin{Bmatrix} i&j &k \\ a_{1}&a_{2} &a_{3} \\ b_{1}&b_{2} &b_{3} \end{Bmatrix}=\left \langle a_{2}b_{3}-a_{3}b_{2}, a_{1}b_{3}-a_{3}b_{1},a_{1}b_{2}-a_{2}b_{1} \right \rangle$ .

Given $a=\left \langle 0,-3,3\right \rangle$ and $b=\left \langle -3,0,3\right \rangle$ , the cross product $a \times b$ is:

$\begin{Bmatrix} i&j &k \\ 0&-3 &3 \\ -3&0 &3 \end{Bmatrix}$

$=\left \langle (-3)(3)-(3)(0), (0)(3)-(3)(-3), (0)(0)-(-3)(-3) \right \rangle$

$=\left \langle -9-0, 0+9, 0-9 \right \rangle$

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

Report an Error

Example Question #561 : Parametric, Polar, And Vector

What is the dot product of $a=\left \langle 3,5,7\right \rangle$ and $b=\left \langle -4,-1,2\right \rangle$ ?

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors is the sum of the products of the vectors' corresponding elements. Given $a=\left \langle 3,5,7\right \rangle$ and $b=\left \langle -4,-1,2\right \rangle$ , then:

$\left \langle 3,5,7\right \rangle\times \left \langle -4,-1,2\right \rangle$

$=(3\times -4)+(5\times -1)+(7\times 2)$

=(-12)+(-5)+(14)

=-17+14

=-3

Report an Error

Example Question #51 : Vector Calculations

What is the dot product of $a=\left \langle 2,0,-2\right \rangle$ and $b=\left \langle 6,1,7\right \rangle$ ?

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors is the sum of the products of the vectors' corresponding elements. Given $a=\left \langle 2,0,-2\right \rangle$ and $b=\left \langle 6,1,7\right \rangle$ then:

$\left \langle 2,0,-2\right \rangle\times \left \langle 6,1,7\right \rangle$

$=(2\times 6)+(0\times 1)+(-2\times7)$

=12+0-14

=-2

Report an Error

View Calculus 2 Tutors

John
Certified Tutor

The University of Texas at Arlington, Bachelor of Science, Mathematics. Stanford University, Master of Science, Aerospace Eng...

View Calculus 2 Tutors

Samantha
Certified Tutor

Middlesex County College, Associate in Science, Sustainability Studies.

View Calculus 2 Tutors

Rodolfo
Certified Tutor

The University of Texas at San Antonio, Bachelor of Science, Mathematics.

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in San Diego, Physics Tutors in Boston, French Tutors in Washington DC, Math Tutors in Philadelphia, Chemistry Tutors in Washington DC, SSAT Tutors in Phoenix, Reading Tutors in San Francisco-Bay Area, SSAT Tutors in Seattle, English Tutors in Philadelphia, Calculus Tutors in Atlanta

Popular Courses & Classes

ISEE Courses & Classes in New York City, SAT Courses & Classes in Washington DC, MCAT Courses & Classes in Philadelphia, SAT Courses & Classes in Atlanta, MCAT Courses & Classes in New York City, LSAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Chicago, SSAT Courses & Classes in Los Angeles, SSAT Courses & Classes in San Diego

Popular Test Prep

GMAT Test Prep in Phoenix, ACT Test Prep in San Diego, GMAT Test Prep in Chicago, LSAT Test Prep in Chicago, SSAT Test Prep in Chicago, GRE Test Prep in Boston, ISEE Test Prep in Atlanta, ACT Test Prep in Seattle, ACT Test Prep in New York City, LSAT 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 2 : Vector Calculations

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #51 : Vector Calculations

Example Question #211 : Vector

Example Question #551 : Parametric, Polar, And Vector

Example Question #51 : Vector Calculations

Example Question #1073 : Calculus Ii

Example Question #1074 : Calculus Ii

Example Question #51 : Vector Calculations

Example Question #1076 : Calculus Ii

Example Question #561 : Parametric, Polar, And Vector

Example Question #51 : Vector Calculations

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: