We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Geometric Vectors

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 #171 : Matrices And Vectors

Subtract: $\left \langle3, 4 \right \rangle - \left \langle -4,-3\right \rangle$ $\displaystyle \left \langle3, 4 \right \rangle - \left \langle -4,-3\right \rangle$

Possible Answers:

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

$\left \langle 7,7\right \rangle$ $\displaystyle \left \langle 7,7\right \rangle$

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

$\left \langle -1,1\right \rangle$ $\displaystyle \left \langle -1,1\right \rangle$

$\left \langle 1,-1\right \rangle$ $\displaystyle \left \langle 1,-1\right \rangle$

Correct answer:

$\left \langle 7,7\right \rangle$ $\displaystyle \left \langle 7,7\right \rangle$

Explanation:

Subtract the first value of the first vector, and the second value of the first vector with the second value of the second vector.

$\left \langle3, 4 \right \rangle - \left \langle -4,-3\right \rangle = \left \langle 3-(-4),4-(-3)\right \rangle$ $\displaystyle \left \langle3, 4 \right \rangle - \left \langle -4,-3\right \rangle = \left \langle 3-(-4),4-(-3)\right \rangle$

Double negative signs are converted to a positive sign.

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

Report an Error

Example Question #21 : Geometric Vectors

Simplify: $\left \langle 2,-3,4\right \rangle+\left \langle-3,-3 \right \rangle-\left \langle5 \right \rangle$ $\displaystyle \left \langle 2,-3,4\right \rangle+\left \langle-3,-3 \right \rangle-\left \langle5 \right \rangle$

Possible Answers:

$\left \langle -1,0,-1\right \rangle$ $\displaystyle \left \langle -1,0,-1\right \rangle$

$\left \langle -6,-6,4\right \rangle$ $\displaystyle \left \langle -6,-6,4\right \rangle$

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

$\left \langle -8\right \rangle$ $\displaystyle \left \langle -8\right \rangle$

$\textup{ Cannot be solved.}$

Correct answer:

$\textup{ Cannot be solved.}$

Explanation:

The dimensions of the vectors are not the same. Placeholders cannot be added to a vector. Therefore, the values of the vectors cannot be added.

The correct answer is: $\textup{ Cannot be solved.}$

Report an Error

Example Question #21 : Geometric Vectors

Find the norm of the vector $\vec{v}=[2,4,3]$ $\displaystyle \vec{v}=[2,4,3]$ .

Possible Answers:

$\left | \vec{v}\right |= \sqrt{29}\approx 5.385$ $\displaystyle \left | \vec{v}\right |= \sqrt{29}\approx 5.385$

$\left | \vec{v}\right |= \sqrt{9} = 3$ $\displaystyle \left | \vec{v}\right |= \sqrt{9} = 3$

$\left | \vec{v}\right |= 2\sqrt{6}\approx 4.899$ $\displaystyle \left | \vec{v}\right |= 2\sqrt{6}\approx 4.899$

$\left | \vec{v}\right |= 9$ $\displaystyle \left | \vec{v}\right |= 9$

Correct answer:

$\left | \vec{v}\right |= \sqrt{29}\approx 5.385$ $\displaystyle \left | \vec{v}\right |= \sqrt{29}\approx 5.385$

Explanation:

We find the norm of a vector by finding the sum of each element squared and then taking the square root.

$\left | \vec{v} \right |= \sqrt{2^2+4^2+3^2}=\sqrt{29}$ $\displaystyle \left | \vec{v} \right |= \sqrt{2^2+4^2+3^2}=\sqrt{29}$ .

Report an Error

Example Question #22 : Geometric Vectors

Find the norm of the vector $\vec{r}=7\hat{i} +4 \hat{j}+5 \hat{k}$ $\displaystyle \vec{r}=7\hat{i} +4 \hat{j}+5 \hat{k}$ .

Possible Answers:

$\left | \vec{r} \ \right | = 3 \sqrt{10}$ $\displaystyle \left | \vec{r} \ \right | = 3 \sqrt{10}$

$\left | \vec{r}\right | = 2 \sqrt{13}$ $\displaystyle \left | \vec{r}\right | = 2 \sqrt{13}$

$\left | \vec{r}\right | = 4$ $\displaystyle \left | \vec{r}\right | = 4$

$\left | \vec{r}\right | = 16$ $\displaystyle \left | \vec{r}\right | = 16$

Correct answer:

$\left | \vec{r} \ \right | = 3 \sqrt{10}$ $\displaystyle \left | \vec{r} \ \right | = 3 \sqrt{10}$

Explanation:

We find the norm of a vector by finding the sum of each component squared and then taking the square root of that sum.

$\left | \vec{r}\right | = \sqrt{ 7^2+4^2+5^2 } = \sqrt{ 90 } = 3 \sqrt{10}$ $\displaystyle \left | \vec{r}\right | = \sqrt{ 7^2+4^2+5^2 } = \sqrt{ 90 } = 3 \sqrt{10}$

Report an Error

Example Question #1593 : Pre Calculus

Find the norm of the vector: <3,-12,5.6,2,-9> $\displaystyle < 3,-12,5.6,2,-9>$

Possible Answers:

31.6 $\displaystyle 31.6$

$\sqrt{269.36}\approx 16.41$ $\displaystyle \sqrt{269.36}\approx 16.41$

269.36 $\displaystyle 269.36$

$\sqrt{184.36}\approx 13.58$ $\displaystyle \sqrt{184.36}\approx 13.58$

$\sqrt{31.6}\approx 5.62$ $\displaystyle \sqrt{31.6}\approx 5.62$

Correct answer:

$\sqrt{269.36}\approx 16.41$ $\displaystyle \sqrt{269.36}\approx 16.41$

Explanation:

The norm of a vector is also known as the length of the vector. The norm is given by the formula:

$\sqrt{\sum_{i=1}^nv_i^2}=\left \| v\right \|$ $\displaystyle \sqrt{\sum_{i=1}^nv_i^2}=\left \| v\right \|$ .

Here, we have

$\left \|v \right \|=\sqrt{3^2+(-12)^2+5.6^2+2^2+(-9)^2}=\sqrt{269.36}$ $\displaystyle \left \|v \right \|=\sqrt{3^2+(-12)^2+5.6^2+2^2+(-9)^2}=\sqrt{269.36}$ ,

the correct answer.

Report an Error

Example Question #23 : Geometric Vectors

Find the norm of vector $\left \langle -2,2\right \rangle$ $\displaystyle \left \langle -2,2\right \rangle$ .

Possible Answers:

$\displaystyle 4$

$\displaystyle 2$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\displaystyle 0$

$2\sqrt2$ $\displaystyle 2\sqrt2$

Correct answer:

$2\sqrt2$ $\displaystyle 2\sqrt2$

Explanation:

Write the formula to find the norm, or the length the vector.

$\left \| v\right \|=\sqrt{a_{1}^2+b_{2}^2}$ $\displaystyle \left \| v\right \|=\sqrt{a_{1}^2+b_{2}^2}$

Substitute the known values of the vector and solve.

$\left \| v\right \|=\sqrt{(-2)^2+2^2}= \sqrt{4+4}=\sqrt8=2\sqrt2$ $\displaystyle \left \| v\right \|=\sqrt{(-2)^2+2^2}= \sqrt{4+4}=\sqrt8=2\sqrt2$

Report an Error

Example Question #26 : Geometric Vectors

Find the norm (magnitude) of the following vector:

$\vec{b}=3i+5j-6k$ $\displaystyle \vec{b}=3i+5j-6k$

Possible Answers:

$-\sqrt{70}$ $\displaystyle -\sqrt{70}$

$\sqrt{72}$ $\displaystyle \sqrt{72}$

$\sqrt{70}$ $\displaystyle \sqrt{70}$

$\displaystyle 70$

$\displaystyle 36$

Correct answer:

$\sqrt{70}$ $\displaystyle \sqrt{70}$

Explanation:

Use the following equation to find the magnitude of a vector:

$\left \| \vec{b}\right \|=\sqrt{i^2+j^2+k^2}$ $\displaystyle \left \| \vec{b}\right \|=\sqrt{i^2+j^2+k^2}$

In this case we have:

$\vec{b}=3i+5j-6k$ $\displaystyle \vec{b}=3i+5j-6k$

So plug in our values:

$\left \| \vec{b}\right \|=\sqrt{3^2+5^2+(-6)^2}=\sqrt{70}$ $\displaystyle \left \| \vec{b}\right \|=\sqrt{3^2+5^2+(-6)^2}=\sqrt{70}$

So:

$\left \| \vec{b} \right \|=\sqrt{70}$ $\displaystyle \left \| \vec{b} \right \|=\sqrt{70}$

Report an Error

Example Question #24 : Geometric Vectors

Find the product of the vector $\vec{r}= 11\hat{i}+7\hat{j}$ $\displaystyle \vec{r}= 11\hat{i}+7\hat{j}$ and the scalar a=4 $\displaystyle a=4$ .

Possible Answers:

$a\vec{r}=44 \hat{j}+28\vec{i}$ $\displaystyle a\vec{r}=44 \hat{j}+28\vec{i}$

$a\vec{r}=44 \hat{i}+28\vec{j}$ $\displaystyle a\vec{r}=44 \hat{i}+28\vec{j}$

$a\vec{r}=72$ $\displaystyle a\vec{r}=72$

$a\vec{r}=72 \hat{i}$ $\displaystyle a\vec{r}=72 \hat{i}$

Correct answer:

$a\vec{r}=44 \hat{i}+28\vec{j}$ $\displaystyle a\vec{r}=44 \hat{i}+28\vec{j}$

Explanation:

When multiplying a vector by a scalar we multiply each component of the vector by the scalar and the result is a vector:

$a \vec{r}= 4 \cdot (11 \hat{i} + 7 \hat{j}) = 44 \hat{i}+28 \hat{j}$ $\displaystyle a \vec{r}= 4 \cdot (11 \hat{i} + 7 \hat{j}) = 44 \hat{i}+28 \hat{j}$

Report an Error

View Pre-Calculus Tutors

Ali
Certified Tutor

university of Trieste, Bachelor of Science, Industrial Engineering. University of Huelva, Master of Science, Aircraft Armamen...

View Pre-Calculus Tutors

Thomas
Certified Tutor

Dartmouth College, Bachelor in Arts, Biochemistry and Molecular Biology. Columbia University in the City of New York, Master ...

View Pre-Calculus Tutors

Joseph
Certified Tutor

Rhode Island School of Design, Bachelor in Arts, Painting. Brown University, Bachelor in Arts, Multimedia.

All Precalculus Resources

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

Popular Subjects

English Tutors in San Diego, SAT Tutors in San Francisco-Bay Area, SSAT Tutors in Seattle, Chemistry Tutors in Houston, Biology Tutors in San Diego, SSAT Tutors in San Francisco-Bay Area, Reading Tutors in San Francisco-Bay Area, Computer Science Tutors in Atlanta, Biology Tutors in Seattle, GRE Tutors in San Francisco-Bay Area

Popular Courses & Classes

ISEE Courses & Classes in New York City, MCAT Courses & Classes in Denver, LSAT Courses & Classes in New York City, ISEE Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Miami, GRE Courses & Classes in New York City, GRE Courses & Classes in Denver, LSAT Courses & Classes in Los Angeles, SAT Courses & Classes in Phoenix, SAT Courses & Classes in Atlanta

Popular Test Prep

SSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Denver, MCAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Los Angeles, GRE Test Prep in Denver, ACT Test Prep in Denver, SAT Test Prep in Chicago, LSAT Test Prep in San Diego, SAT Test Prep in Washington DC, GMAT 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

Precalculus : Geometric Vectors

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #171 : Matrices And Vectors

Example Question #21 : Geometric Vectors

Example Question #21 : Geometric Vectors

Example Question #22 : Geometric Vectors

Example Question #1593 : Pre Calculus

Example Question #23 : Geometric Vectors

Example Question #26 : Geometric Vectors

Example Question #24 : Geometric Vectors

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: