Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Number and Quantity : Magnitude and Direction of a Vector Sum: CCSS.Math.Content.HSN-VM.B.4b

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

Create An Account

All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #42 : Vector & Matrix Quantities

If $\left \| v\right \|=10$ , and $\left \| w\right \|=5$ , and the angle in between them is $60^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=\sqrt{75}$

$\left \| v+w\right \|=15$

$\left \| v+w\right \|=\sqrt{85}$

$\left \| v+w\right \|=7$

$\left \| v+w\right \|=\sqrt{65}$

Correct answer:

$\left \| v+w\right \|=\sqrt{75}$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=10 , b=5 , and $C=60^{\circ}$ , then

$c^2=10^2+5^2-2\cdot10\cdot5\cos(60^{\circ})$

$c^2=100+25-20\cdot5\cos(60^{\circ})$

$c^2=125-100\cos(60^{\circ})$

$c^2=125-100\cdot\frac{1}{2}$

c^2=125-50

c^2=75

$\sqrt{c^2}=\sqrt{75}$

$c=\sqrt{75}\approx8.66$

Here is a visual representation of what we just found.

Locs

Report an Error

Example Question #145 : High School: Number And Quantity

If $\left \| v\right \|=11$ , and $\left \| w\right \|=21$ , and the angle in between them is $21^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=11.43$

$\left \| v+w\right \|=12$

$\left \| v+w\right \|=11.6$

$\left \| v+w\right \|=11.5$

$\left \| v+w\right \|=\sqrt{85}$

Correct answer:

$\left \| v+w\right \|=11.43$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=11 , b=21 , and $C=21^{\circ}$ , then

$c^2=11^2+21^2-2\cdot11\cdot21\cos(21^{\circ})$

$c^2=121+441-462\cos(21^{\circ})$

$c^2=562-462\cos(21^{\circ})$

$c^2=562-462\cdot0.9336$

c^2=562-431.3142

c^2=130.6858

$\sqrt{c^2}=\sqrt{130.6858}$

$c=\sqrt{130.6858}\approx11.43$

Report an Error

Example Question #146 : High School: Number And Quantity

If $\left \| v\right \|=8$ , and $\left \| w\right \|=22$ , and the angle in between them is $103^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=21.04$

$\left \| v+w\right \|=24.04$

$\left \| v+w\right \|=22.04$

$\left \| v+w\right \|=25.04$

$\left \| v+w\right \|=23.04$

Correct answer:

$\left \| v+w\right \|=25.04$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=8 , b=22 , and $C=103^{\circ}$ , then

$c^2=8^2+22^2-2\cdot8\cdot22\cos(103^{\circ})$

$c^2=64+484-16\cdot22\cos(103^{\circ})$

$c^2=548-352\cos(103^{\circ})$

$c^2=548-352\cdot-0.2249511$

c^2=548+79.18277

c^2=627.1828

$\sqrt{c^2}=\sqrt{627.1828}$

$c=\sqrt{627.1828}\approx25.04$

Report an Error

Example Question #147 : High School: Number And Quantity

If $\left \| v\right \|=1$ , and $\left \| w\right \|=38$ , and the angle in between them is $116^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=38.45$

$\left \| v+w\right \|=38.5$

$\left \| v+w\right \|=40.8$

$\left \| v+w\right \|=38.6$

$\left \| v+w\right \|=41.34$

Correct answer:

$\left \| v+w\right \|=38.45$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=1 , b=38 , and $C=116^{\circ}$ , then

$c^2=1^2+38^2-2\cdot1\cdot38\cos(116^{\circ})$

$c^2=1+1444-2\cdot38\cos(116^{\circ})$

$c^2=1445-76\cos(116^{\circ})$

$c^2=1445-76\cdot-.4383711$

c^2=1445+33.31621

c^2=1478.316

$\sqrt{c^2}=\sqrt{1478.316}$

$c=\sqrt{1478.316}\approx38.45$

Report an Error

Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=18$ , and $\left \| w\right \|=16$ , and the angle in between them is $26^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=7.89$

$\left \| v+w\right \|=4.67$

$\left \| v+w\right \|=20.27$

$\left \| v+w\right \|=11.43$

$\left \| v+w\right \|=9.62$

Correct answer:

$\left \| v+w\right \|=7.89$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=10 , b=5 , and $C=60^{\circ}$ , then

$c^2=18^2+16^2-2\cdot18\cdot16\cos(26^{\circ})$

$c^2=324+256-36\cdot16\cos(26^{\circ})$

$c^2=580-576\cos(26^{\circ})$

c^2=580-517.7054

c^2=62.2946

$\sqrt{c^2}=\sqrt{62.2946}$

$c=\sqrt{62.2946}\approx7.89$

Report an Error

Example Question #149 : High School: Number And Quantity

If $\left \| v\right \|=16$ , and $\left \| w\right \|=19$ , and the angle in between them is $150^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=31.42$

$\left \| v+w\right \|=36.87$

$\left \| v+w\right \|=40.58$

$\left \| v+w\right \|=33.82$

$\left \| v+w\right \|=30.8$

Correct answer:

$\left \| v+w\right \|=33.82$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=16 , b=19 , and $C=150^{\circ}$ , then

$c^2=16^2+19^2-2\cdot16\cdot19\cos(150^{\circ})$

$c^2=256+361-32\cdot19\cos(150^{\circ})$

$c^2=617-608\cos(150^{\circ})$

$c^2=617-608\cdot-0.8660254$

c^2=1143.543

$\sqrt{c^2}=\sqrt{1143.543}$

$c=\sqrt{1143.543}\approx33.82$

Report an Error

Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=34$ , and $\left \| w\right \|=17$ , and the angle in between them is $10^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=13.56$

$\left \| v+w\right \|=17.51$

$\left \| v+w\right \|=18.09$

$\left \| v+w\right \|=14.69$

$\left \| v+w\right \|=17.84$

Correct answer:

$\left \| v+w\right \|=17.51$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=17 , b=10 , and $C=10^{\circ}$ , then

$c^2=17^2+34^2-2\cdot34\cdot17\cos(10^{\circ})$

$c^2=289+1156-34\cdot34\cos(10^{\circ})$

$c^2=1445-1156\cos(10^{\circ})$

c^2=1445-1138.438

c^2=306.562

$\sqrt{c^2}=\sqrt{306.562}$

$c=\sqrt{306.562}\approx17.51$

Report an Error

Example Question #2 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=18$ , and $\left \| w\right \|=19$ , and the angle in between them is $131^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=33.67$

$\left \| v+w\right \|=32.89$

$\left \| v+w\right \|=34.90$

$\left \| v+w\right \|=37.92$

$\left \| v+w\right \|=31.56$

Correct answer:

$\left \| v+w\right \|=33.67$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=18 , b=2 , and $C=106^{\circ}$ , then

$c^2=18^2+19^2-2\cdot18\cdot19\cos(131^{\circ})$

$c^2=324+361-36\cdot19\cos(131^{\circ})$

$c^2=685-684\cos(131^{\circ})$

$c^2=685-684\cdot-0.656059$

c^2=685+448.7444

c^2=1133.744

$\sqrt{c^2}=\sqrt{1133.744}$

$c=\sqrt{1133.744}\approx33.67$

Report an Error

Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=4$ , and $\left \| w\right \|=23$ , and the angle in between them is $149^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=28.13$

$\left \| v+w\right \|=27.76$

$\left \| v+w\right \|=27.23$

$\left \| v+w\right \|=24.57$

$\left \| v+w\right \|=26.42$

Correct answer:

$\left \| v+w\right \|=27.23$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=4 , b=23 , and $C=149^{\circ}$ , then

$c^2=4^2+23^2-2\cdot4\cdot23\cos(149^{\circ})$

$c^2=16+529-8\cdot23\cos(149^{\circ})$

$c^2=545-184\cos(149^{\circ})$

$c^2=545-184\cdot-0.8571673$

c^2=584+157.7188

c^2=741.7188

$\sqrt{c^2}=\sqrt{741.7188}$

$c=\sqrt{741.7188}\approx27.23$

Report an Error

Example Question #4 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=14$ , and $\left \| w\right \|=1$ , and the angle in between them is $76^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=14.09$

$\left \| v+w\right \|=13.79$

$\left \| v+w\right \|=17.94$

$\left \| v+w\right \|=14.25$

$\left \| v+w\right \|=13.62$

Correct answer:

$\left \| v+w\right \|=13.79$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=14 , b=1 , and $C=76^{\circ}$ , then

$c^2=14^2+1^2-2\cdot14\cdot1\cos(76^{\circ})$

$c^2=196+1-28\cdot1\cos(76^{\circ})$

$c^2=197-28\cos(76^{\circ})$

$c^2=197-28\cdot0.2419219$

c^2=197-6.773813

c^2=190.2262

$\sqrt{c^2}=\sqrt{190.2262}$

$c=\sqrt{190.2262}\approx13.79$

Report an Error

View Tutors

Sophia
Certified Tutor

University of Houston, Bachelor in Arts, History.

View Tutors

Steven
Certified Tutor

University of Waterloo, Bachelor of Science, Chemical Engineering. McMaster University, Master of Science, Chemical Engineeri...

View Tutors

Jahlen
Certified Tutor

SUNY at Purchase College, Bachelor in Arts, Economics.

All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Seattle, Physics Tutors in Denver, Computer Science Tutors in Houston, MCAT Tutors in Philadelphia, GMAT Tutors in Miami, Reading Tutors in New York City, LSAT Tutors in Washington DC, Statistics Tutors in San Francisco-Bay Area, Reading Tutors in Los Angeles, Reading Tutors in Washington DC

Popular Courses & Classes

SSAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Los Angeles, ISEE Courses & Classes in Washington DC, MCAT Courses & Classes in Los Angeles, ISEE Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in New York City, ACT Courses & Classes in Los Angeles, LSAT Courses & Classes in Washington DC, ISEE Courses & Classes in New York City, SSAT Courses & Classes in San Diego

Popular Test Prep

MCAT Test Prep in Denver, ACT Test Prep in Dallas Fort Worth, SAT Test Prep in Seattle, SAT Test Prep in Dallas Fort Worth, GRE Test Prep in Dallas Fort Worth, GMAT Test Prep in Chicago, SSAT Test Prep in Chicago, GRE Test Prep in Denver, ISEE Test Prep in Phoenix, ACT Test Prep in Chicago

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

Common Core: High School - Number and Quantity : Magnitude and Direction of a Vector Sum: CCSS.Math.Content.HSN-VM.B.4b

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #42 : Vector & Matrix Quantities

Example Question #145 : High School: Number And Quantity

Example Question #146 : High School: Number And Quantity

Example Question #147 : High School: Number And Quantity

Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #149 : High School: Number And Quantity

Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #2 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #4 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

All Common Core: High School - Number and Quantity Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: