We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Vectors

Study concepts, example questions & explanations for GRE Subject Test: Math

Create An Account

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Vectors

Calculate the dot product of the following vectors:

$a=\left \langle c,6, s\right \rangle$

$b=\left \langle c,10,s\right \rangle$

Possible Answers:

c^2+16+s^2

c^2+60+s^2

2cs+60

2c+16+2s

60c^2s^2

Correct answer:

c^2+60+s^2

Explanation:

Write the formula for dot product given $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ and $b=\left \langle b_{1},b_{2},b_{3}\right \rangle$ .

$a\cdot b= a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}$

Substitute the values of the vectors to determine the dot product.

$a\cdot b= c(c)+(6)(10)+s(s) = c^2+60+s^2$

Report an Error

Example Question #1 : Vector Form

Express -i-k in vector form.

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

The correct form of x,y, and z of a vector is represented in the order of i, j, and k, respectively. The coefficients of i,j, and k are used to write the vector form.

$-i-k = -1i+0j-1k = \left \langle -1,0,-1\right \rangle$

Report an Error

Example Question #1 : Vectors

Express -10j in vector form.

Possible Answers:

$\left \langle 1,-10,1\right \rangle$

$\left \langle -10,-10,-10\right \rangle$

$\left \langle -10,0,0\right \rangle$

$\left \langle 0,0,-10\right \rangle$

$\left \langle 0,-10,0\right \rangle$

Correct answer:

$\left \langle 0,-10,0\right \rangle$

Explanation:

The x,y, and z of a vector is represented in the order of i, j, and k, respectively. Use the coefficients of i,j, and k to write the vector form.

$-10j=0i-10j+0k = \left \langle 0,-10,0\right \rangle$

Report an Error

Example Question #1 : Vector Form

Find the vector form of (6,3,1) to (0,1,3) .

Possible Answers:

$\overrightarrow{v}=[6,2,-3]$

$\overrightarrow{v}=[-6,-2,-2]$

$\overrightarrow{v}=[6,2,2]$

$\overrightarrow{v}=[6,-2,-2]$

$\overrightarrow{v}=[6,2,-2]$

Correct answer:

$\overrightarrow{v}=[6,2,-2]$

Explanation:

When we are trying to find the vector form we need to remember the formula which states to take the difference between the ending and starting point.

Thus we would get:

Given (a,b,c) and (d,e,f)

$\overrightarrow{v}=[d-a, e-b, f-c]$

In our case we have ending point at (6,3,1) and our starting point at (0,1,3) .

Therefore we would set up the following and simplify.

$\overrightarrow{v}=[6-0,3-1,1-3]=[6,2,-2]$

Report an Error

Example Question #25 : Linear Algebra

Find the dot product of the 2 vectors. $\left \langle a,2a\right \rangle \cdot \left \langle a,a\right \rangle$

Possible Answers:

$\left \langle a^2,2a^2\right \rangle$

$\left \langle 3a^2,3a^2\right \rangle$

$\left \langle a,2a\right \rangle$

3a^2

Correct answer:

3a^2

Explanation:

The dot product will give a single value answer, and not a vector as a result.

To find the dot product, use the following formula:

$\left \langle x_1,x_2\right \rangle \cdot \left \langle y_1,y_2\right \rangle=(x_1)(y_1)+(x_2)(y_2)$

$\left \langle a,2a\right \rangle \cdot \left \langle a,a\right \rangle = (a)(a)+(2a)(a)=a^2+2a^2=3a^2$

Report an Error

Example Question #2 : Vectors & Spaces

Assume that Billy fired himself out of a circus cannon at a velocity of $25 \:mph$ at an elevation angle of degrees. Write this in vector component form.

Possible Answers:

$\left \langle22.658,10.565 \right \rangle$

$\left \langle 25.25,25.25\right \rangle$

$\left \langle23.097, 9.567 \right \rangle$

$\left \langle 50,50\right \rangle$

$\left \langle 24.78,-3.309\right \rangle$

Correct answer:

$\left \langle22.658,10.565 \right \rangle$

Explanation:

The firing of the cannon has both x and y components.

Write the formula that distinguishes the x and y direction and substitute.

$\left \langle x,y\right \rangle= \left \langle vcos(\theta),vsin(\theta)\right \rangle$

Ensure that the calculator is in degree mode before you solve.

$\left \langle 25cos25,25sin25\right \rangle = \left \langle22.658,10.565 \right \rangle$

Report an Error

Example Question #1 : Vectors

Compute: $2\vec{a}-6\vec{b}$ given the following vectors. $\vec{a}= \left \langle 1,3\right \rangle$ and $\vec{b}= \left \langle 1\right \rangle$ .

Possible Answers:

$\left \langle -4,0\right \rangle$

${}\left< \sqrt{13} \right \rangle$

The answer does not exist.

$\left \langle 1,2\right \rangle$

$\left \langle -4,3\right \rangle$

Correct answer:

The answer does not exist.

Explanation:

The dimensions of the vectors are mismatched.

Since vector $\vec{a}$ does not have the same dimensions as $\vec{b}$ , the answer for $2\vec{a}-6\vec{b}$ cannot be solved.

Report an Error

Example Question #1 : Vector Form

What is the vector form of 2i-10k ?

Possible Answers:

$\left \langle 2,0,-10\right \rangle$

$\left \langle -10,2,0\right \rangle$

$\left \langle 2,-10,0\right \rangle$

Correct answer:

$\left \langle 2,0,-10\right \rangle$

Explanation:

To find the vector form of 2i-10k , we must map the coefficients of , , and to their corresponding , , and coordinates. Thus, 2i-10k becomes $\left \langle 2,0,-10\right \rangle$ .

Report an Error

Example Question #1 : Vector Form

Express -2i+7j-10k in vector form.

Possible Answers:

$\left \langle 2,-7,10\right \rangle$

$\left \langle -2,-7,-10\right \rangle$

$\left \langle 2,7,-10\right \rangle$

$\left \langle -2,7,-10\right \rangle$

$\left \langle 2,7,10\right \rangle$

Correct answer:

$\left \langle -2,7,-10\right \rangle$

Explanation:

In order to express -2i+7j-10k in vector form, we must use the coefficients of i, j, and to represent the -, -, and -coordinates of the vector.

Therefore, its vector form is

$\left \langle -2,7,-10\right \rangle$ .

Report an Error

Example Question #1 : Vector Form

Express i+5k in vector form.

Possible Answers:

$\left \langle -1,5\right \rangle$

$\left \langle -1,-5\right \rangle$

$\left \langle -1,0,5\right \rangle$

$\left \langle 1,5\right \rangle$

$\left \langle 1,0,5\right \rangle$

Correct answer:

$\left \langle 1,0,5\right \rangle$

Explanation:

In order to express i+5k in vector form, we must use the coefficients of i, j, and to represent the -, -, and -coordinates of the vector.

Therefore, its vector form is

$\left \langle 1,0,5\right \rangle$ .

Report an Error

View Tutors

Samuel
Certified Tutor

York University, Bachelor, Physics. York University, Master's/Graduate, Mathematics and Statistics.

View Tutors

Sumit
Certified Tutor

Calcutta University, Bachelor of Science, Mathematics. Indian Statistical Institute, Master of Science, Mathematics.

View Tutors

Samarth
Certified Tutor

Maharaja Sayajirao University of Baroda, Bachelor of Engineering, Mechanical Engineering. Concordia University-Seward, Master...

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Dallas Fort Worth, Biology Tutors in Los Angeles, French Tutors in New York City, French Tutors in Philadelphia, Algebra Tutors in Chicago, Spanish Tutors in Chicago, English Tutors in Atlanta, SAT Tutors in Phoenix, MCAT Tutors in San Diego, LSAT Tutors in Denver

Popular Courses & Classes

SAT Courses & Classes in Philadelphia, ACT Courses & Classes in Miami, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Atlanta, GMAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Washington DC, ISEE Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Miami, ACT Courses & Classes in San Diego, GMAT Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in Houston, LSAT Test Prep in Miami, MCAT Test Prep in Boston, SSAT Test Prep in Denver, SAT Test Prep in Philadelphia, ACT Test Prep in Seattle, GMAT Test Prep in Los Angeles, ISEE Test Prep in Chicago, SAT Test Prep in Boston, ACT Test Prep in San Diego

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

GRE Subject Test: Math : Vectors

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Vectors

Example Question #1 : Vector Form

Example Question #1 : Vectors

Example Question #1 : Vector Form

Example Question #25 : Linear Algebra

Example Question #2 : Vectors & Spaces

Example Question #1 : Vectors

Example Question #1 : Vector Form

Example Question #1 : Vector Form

Example Question #1 : Vector Form

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: