We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Algebra

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

← Previous 1 2 … 22 23 24 25 26 27 28 29 30 31 32 Next →

Example Question #77 : Linear Algebra

Find the vector in standard form if the initial point is located at (3,7) and the terminal point is located at (7,10) .

Possible Answers:

i+j

-4i-3j

7i+3j

4i+3j

Correct answer:

4i+3j

Explanation:

We must first find the vector in component form.

If the initial point is (p_1,p_2) and the terminal point is (q_1,q_2) then the component form of the vector is $\left<q_1-p_1,q_2-p_2\right>$ .

As such, the component form of the vector in the problem is $\left<7-3,10-7\right>$ $=\left<4,3\right>$

Next, any vector with component form $\left<a,b\right>$ can be written in standard form as ai+bj .

Hence, the vector in standard form is

4i+3j

Report an Error

Example Question #71 : Linear Algebra

What is the vector form of 3i-5j+7k ?

Possible Answers:

$\left \langle -3,-5,7\right \rangle$

$\left \langle 3,-5,7\right \rangle$

$\left \langle -3,5,7\right \rangle$

$\left \langle -3,-5,-7\right \rangle$

$\left \langle 3,5,-7\right \rangle$

Correct answer:

$\left \langle 3,-5,7\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ .

So for 3i-5j+7k , we can derive the vector form $\left \langle 3,-5,7\right \rangle$ .

Report an Error

Example Question #79 : Linear Algebra

What is the vector form of ?

Possible Answers:

$\left \langle 7,0,0\right \rangle$

$\left \langle 0,0,-7\right \rangle$

$\left \langle -7,0,0\right \rangle$

$\left \langle 0,0,7\right \rangle$

$\left \langle 0,7,0,\right \rangle$

Correct answer:

$\left \langle 7,0,0\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ .

So for , we can derive the vector form $\left \langle 7,0,0\right \rangle$ .

Report an Error

Example Question #80 : Linear Algebra

Given points (9,4,-1) and (5,2,7) , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle -4,2,8\right \rangle$

$\left \langle -4,-2,8\right \rangle$

$\left \langle 4,-2,8\right \rangle$

$\left \langle 4,2,8\right \rangle$

$\left \langle -4,-2,-8\right \rangle$

Correct answer:

$\left \langle -4,-2,8\right \rangle$

Explanation:

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points.

That is, for any point

$a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ ,

the distance is the vector

$v=\left \langle b_1-a_1,b_2-a_2,b_3-a_3\right \rangle$ .

Subbing in our original points (9,4,-1) and (5,2,7) , we get:

$v=\left \langle 5-9,2-4,7-(-1)\right \rangle$

$v=\left \langle -4,-2,8\right \rangle$

Report an Error

Example Question #61 : Vectors

What is the vector form of -6j ?

Possible Answers:

$\left \langle -6, 0,0 \right \rangle$

$\left \langle 0,-6,0 \right \rangle$

$\left \langle 6, 0,0 \right \rangle$

$\left \langle 0,0,-6 \right \rangle$

$\left \langle 0,6,0 \right \rangle$

Correct answer:

$\left \langle 0,-6,0 \right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ .

So for -6j , we can derive the vector form $\left \langle 0,-6,0 \right \rangle$ .

Report an Error

Example Question #62 : Vectors

Given points (0,1,3) and (5,7,4) , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle 5,6,1\right \rangle$

$\left \langle -5,6,1\right \rangle$

$\left \langle -5,-6,-1\right \rangle$

$\left \langle 5,-6,1\right \rangle$

$\left \langle -5,-6,1\right \rangle$

Correct answer:

$\left \langle 5,6,1\right \rangle$

Explanation:

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points.

That is, for any point

$a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ ,

the distance is the vector

$v=\left \langle b_1-a_1,b_2-a_2,b_3-a_3\right \rangle$ .

Subbing in our original points (0,1,3) and (5,7,4) , we get:

$v=\left \langle 5-0,7-1,4-3\right \rangle$

$v=\left \langle 5,6,1\right \rangle$

Report an Error

Example Question #31 : Parametric, Polar, And Vector Functions

Given points (2,4,5) and (9,1,0) , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle -7,3,-5\right \rangle$

$\left \langle 7,3,5\right \rangle$

$\left \langle -7,-3,-5\right \rangle$

$\left \langle 7,-3,-5\right \rangle$

$\left \langle 7,3,-5\right \rangle$

Correct answer:

$\left \langle 7,-3,-5\right \rangle$

Explanation:

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points.

That is, for any point

$a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ ,

the distance is the vector

$v=\left \langle b_1-a_1,b_2-a_2,b_3-a_3\right \rangle$ .

Subbing in our original points (2,4,5) and (9,1,0) , we get:

$v=\left \langle 9-2,1-4,0-5\right \rangle$

$v=\left \langle 7,-3,-5\right \rangle$

Report an Error

Example Question #63 : Vectors

Given points (0,0,-4) and (4,9,-1) , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle -4,9,3\right \rangle$

$\left \langle 4,-9,3\right \rangle$

$\left \langle 4,9,-3\right \rangle$

$\left \langle 4,9,3\right \rangle$

$\left \langle -4,9,-3\right \rangle$

Correct answer:

$\left \langle 4,9,3\right \rangle$

Explanation:

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points. That is, for any point $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , the distance is the vector $v=\left \langle b_1-a_1,b_2-a_2,b_3-a_3\right \rangle$ .

Subbing in our original points (0,0,-4) and (4,9,-1) , we get:

$v=\left \langle 4-0,9-0,-1+4\right \rangle$

$v=\left \langle 4,9,3\right \rangle$

Report an Error

Example Question #251 : Algebra

What is the derivative of the vector function

$r(t)=(\cos t, \sin t)$ ?

Possible Answers:

$r'(t) = (-\sin t,\cos t)$

$r'(t) = (\sin t,\cos t)$

$r'(t) = (\sin t,-\cos t)$

$r'(t) = (-\cos t,\sin t)$

Correct answer:

$r'(t) = (-\sin t,\cos t)$

Explanation:

The derivative of a vector function has its components consisting of the derivatives of its components:

$r'(t) = (-\sin t,\cos t)$

since the derivatives of $\cos t, \sin t$ are $-\sin t, \cos t$ , respectively.

Report an Error

Example Question #65 : Vectors

Given the vector function

r(t)=(t,t^2,t^3)

what is the derivative of the vector function?

Possible Answers:

r'(t)=(3t^2,2t,1)

r'(t)=(1,2t,3t^2)

r'(t)=(0,2,6t)

r'(t)=(t^2/2,t^3/3,t^4/4)

Correct answer:

r'(t)=(1,2t,3t^2)

Explanation:

The derivative of a vector function is just the derivative of components:

r'(t)=(f_1'(t),f_2'(t),f_3'(t))=(1,2t,3t^2)

The derivative of each component was found using the power rule which states,

$x^n dx=nx^{n-1}$ .

Thus,

$t\ dt=1\cdot t^{1-1}=1\cdot t^0=1$ ,

$t^2dt=2t^{2-1}=2t^1=2t$ ,

$t^3dt=3t^{3-1}=3t^2$ .

Report an Error

← Previous 1 2 … 22 23 24 25 26 27 28 29 30 31 32 Next →

View Tutors

Sonu
Certified Tutor

Rajasthan Technical University Kota, Bachelor, Electrical.

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Edmund
Certified Tutor

University of Ghana, Bachelor of Science, Statistics. university of Ghana, Master of Philosophy, Statistics.

All GRE Subject Test: Math Resources

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

Popular Subjects

Math Tutors in Washington DC, MCAT Tutors in Atlanta, Reading Tutors in Seattle, GMAT Tutors in Dallas Fort Worth, MCAT Tutors in Houston, English Tutors in Denver, ISEE Tutors in San Francisco-Bay Area, Biology Tutors in Houston, Physics Tutors in Miami, LSAT Tutors in New York City

Popular Courses & Classes

MCAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in New York City, ISEE Courses & Classes in Miami, GRE Courses & Classes in Houston, LSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Boston, ISEE Courses & Classes in Seattle, GMAT Courses & Classes in Washington DC, ACT Courses & Classes in Boston, MCAT Courses & Classes in Houston

Popular Test Prep

LSAT Test Prep in Los Angeles, SSAT Test Prep in Philadelphia, ISEE Test Prep in Miami, GMAT Test Prep in Washington DC, GRE Test Prep in Boston, ISEE Test Prep in Phoenix, SAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Miami, MCAT Test Prep in Dallas Fort Worth, 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

GRE Subject Test: Math : Algebra

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #77 : Linear Algebra

Example Question #71 : Linear Algebra

Example Question #79 : Linear Algebra

Example Question #80 : Linear Algebra

Example Question #61 : Vectors

Example Question #62 : Vectors

Example Question #31 : Parametric, Polar, And Vector Functions

Example Question #63 : Vectors

Example Question #251 : Algebra

Example Question #65 : Vectors

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: