Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Find the Unit Vector in the Same Direction as a Given Vector

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Find the unit vector that is in the same direction as the vector $\vec{v}= [3,6,1]$

Possible Answers:

$\vec{u}_v= \left [ {\frac{3}{\sqrt{46}}},\frac{6}{\sqrt{46}} , \frac{1}{\sqrt{46}} \right ]$

$\vec{u}_v= \left [ 9,36,1 \right ]$

$\vec{u}_v= \left [ 9,3,1 \right ]$

$\vec{u}_v= \left [ {\frac{9}{\sqrt{3}}},\frac{36}{\sqrt{6}} ,1 \right ]$

Correct answer:

$\vec{u}_v= \left [ {\frac{3}{\sqrt{46}}},\frac{6}{\sqrt{46}} , \frac{1}{\sqrt{46}} \right ]$

Explanation:

To find the unit vector in the same direction as a vector, we divide it by its magnitude.

The magnitude of $\vec{v}$ is $\left | \vec{v} \right |= \sqrt{3^2+6^2+1^2}=\sqrt{46}$ .

We divide vector $\vec{v}$ by its magnitude to get the unit vector $\vec{u}_v$ :

$\vec{u}_v= \frac{\vec{v}}{\left | \vec{v} \right |}=\frac{1}{\sqrt{46}}\cdot[3,6,1]$

$\vec{u}_v= \left [ {\frac{3}{\sqrt{46}}},\frac{6}{\sqrt{46}} , \frac{1}{\sqrt{46}} \right ]$

All unit vectors have a magnitude of , so to verify we are correct:

$\left | \vec{u}_v \right | = \sqrt{ (\frac{3}{\sqrt{46}})^2 + (\frac{6}{\sqrt{46}})^2 + (\frac{9}{\sqrt{46}})^2 } = \sqrt{\frac{9}{46} + \frac{36}{46} + \frac{1}{46} } = 1$

Report an Error

Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

A unit vector has length .

Given the vector

v=<3,6,44,-5,12>

find the unit vector in the same direction.

Possible Answers:

$<\frac{3}{44},\frac{3}{22},1,\frac{-5}{44},\frac{3}{11}>$

<3,6,44,-5,12>

$<1,2,\frac{44}{3},\frac{-5}{3},4>$

<0.065,0.129,0.949,-0.108,0.259>

$<\frac{1}{2},1,\frac{22}{3},\frac{-5}{6},2>$

Correct answer:

<0.065,0.129,0.949,-0.108,0.259>

Explanation:

First, you must find the length of the vector. This is given by the equation:

$\sqrt{3^2+6^2+44^2+(-5)^2+12^2}=\left \| v\right \|$

Then, dividing the vector by its length gives the unit vector in the same direction.

$\frac{v}{\left \| v\right \|}=\frac{<3,6,44,-5,12>}{\sqrt{2150}}\\ \\ \approx<0.065,0.129,0.949,-0.108,0.259>$

Report an Error

Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Put the vector $\small (1,3)$ in unit vector form.

Possible Answers:

$\small (3,1)$

$\left (\frac{1}{10},\frac{3}{10}\right)$

$\left (\frac{3}{\sqrt{10}},\frac{1}{\sqrt{10}}\right)$

$\left (\frac{3}{10},\frac{1}{10}\right)$

$\left (\frac{1}{\sqrt{10}},\frac{3}{\sqrt{10}}\right)$

Correct answer:

$\left (\frac{1}{\sqrt{10}},\frac{3}{\sqrt{10}}\right)$

Explanation:

To get the unit vector that is in the same direction as the original vector $\small v$ , we divide the vector by the magnitude of the vector.

For $\small (1,3)$ , the magnitude is:

$\sqrt{x^2+y^2}$

$\small \sqrt{1^2+3^2}=\sqrt{10}$ .

This means the unit vector in the same direction of $\small (1,3)$ is,

$\small \frac{1}{\sqrt{10}}(1,3)=\left(\frac{1}{\sqrt{10}},\frac{3}{\sqrt{10}}\right)$ .

Report an Error

Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Find the unit vector of

$\left<3,\,4\right>$ .

Possible Answers:

$\left<1,3\right>$

$\left<1,1\right>$

$\left<1,0\right>$

$\left<\frac{3}{5},\, \frac{4}{5}\right>$

Correct answer:

$\left<\frac{3}{5},\, \frac{4}{5}\right>$

Explanation:

In order to find the unit vector u of a given vector v, we follow the formula

$u=\frac{v}{\left | v\right |}$

Let

$v=\left<a,b\right>$

The magnitude of v follows the formula

$\left | v\right |=\sqrt{a^{2}+b^{2}}$ .

For this vector in the problem

$\left | v\right |=\sqrt{3^{2}+4^{2}}$

$=\sqrt{9+16}$

$=\sqrt{25}$

$\left | v\right |=5$ .

Following the unit vector formula and substituting for the vector and magnitude

$u=\frac{\left< 3,4\right>}{5}$ .

As such,

$u\,=\,\left<\frac{3}{5},\, \frac{4}{5}\right>$ .

Report an Error

Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Find the unit vector of

$\left<5,\,12\right>$

Possible Answers:

$\left<1, \frac{12}{5}\right>$

$\left<\frac{1}{2},\frac{1}{2}\right>$

$\left<2,1\right>$

$\left<\frac{5}{13},\,\frac{12}{13}\right>$

Correct answer:

$\left<\frac{5}{13},\,\frac{12}{13}\right>$

Explanation:

In order to find the unit vector u of a given vector v, we follow the formula

$u=\frac{v}{\left | v\right |}$

Let

$v=\left<a,b\right>$

The magnitude of v follows the formula

$\left | v\right |=\sqrt{a^{2}+b^{2}}$

For this vector in the problem

$\left | v\right |=\sqrt{5^{2}+12^{2}}$

$=\sqrt{25+144}$

$=\sqrt{169}$

$\left | v\right |=13$

Following the unit vector formula and substituting for the vector and magnitude

$u=\frac{\left< 5,12\right>}{13}$

As such,

$u\,=\,\left<\frac{5}{13},\, \frac{12}{13}\right>$

Report an Error

View Pre-Calculus Tutors

Sydney
Certified Tutor

University of Vermont, Bachelor of Science, Nursing (RN). University of Connecticut, Bachelor of Science, Health Sciences, Ge...

View Pre-Calculus Tutors

James
Certified Tutor

St. Mary of the Plains College, Bachelors, Mathematics. Baker University, Masters, Business Administration and Management.

View Pre-Calculus Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in Los Angeles, Math Tutors in Denver, MCAT Tutors in San Francisco-Bay Area, Algebra Tutors in New York City, SSAT Tutors in Atlanta, SSAT Tutors in Houston, ACT Tutors in Dallas Fort Worth, ISEE Tutors in Dallas Fort Worth, Statistics Tutors in Phoenix, Biology Tutors in Seattle

Popular Courses & Classes

GRE Courses & Classes in Washington DC, Spanish Courses & Classes in Miami, GMAT Courses & Classes in Philadelphia, GRE Courses & Classes in Miami, MCAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Phoenix, LSAT Courses & Classes in San Diego, SSAT Courses & Classes in Boston

Popular Test Prep

ISEE Test Prep in Seattle, SAT Test Prep in Seattle, GMAT Test Prep in Philadelphia, LSAT Test Prep in Philadelphia, GRE Test Prep in New York City, SSAT Test Prep in Atlanta, LSAT Test Prep in Denver, GRE Test Prep in Chicago, MCAT Test Prep in Dallas Fort Worth, GMAT 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

Precalculus : Find the Unit Vector in the Same Direction as a Given Vector

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: