We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Pre-Calculus

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 A Direction Vector When Given Two Points

Find $\overrightarrow{MN}$ if N=(2, 2) and M=(-2, 1) .

Possible Answers:

<-4, -1>

<1, -4>

<4,1>

<4, -1>

Correct answer:

<4,1>

Explanation:

To find the direction vector from to , subtract the x- and y-coordinates of from .

$\overrightarrow{MN}=<2-(-2), 2-1>=<4, 1>$

Report an Error

Example Question #1 : Find A Direction Vector When Given Two Points

Find the direction vector that has an initial point at C(1,5) and a terminal point of D(0, 1) .

Possible Answers:

<-4, -1>

<-1, -4>

<1, 4>

<-4, 1>

Correct answer:

<-1, -4>

Explanation:

To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

$\overrightarrow{CD}=<0-1, 1-5>=<-1, -4>$

Report an Error

Example Question #1 : Find A Direction Vector When Given Two Points

Find the direction vector that has an initial point at E(4, 1) and a terminal point at F(-5, -1) .

Possible Answers:

<-2, -9>

<2, 9>

<9, 2>

<-9, -2>

Correct answer:

<-9, -2>

Explanation:

To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

$\overrightarrow{EF}=<-5-4, -1-1>=<-9, -2>$

Report an Error

Example Question #1 : Find A Direction Vector When Given Two Points

Find the direction vector with an initial point of R(-1, 4) and an terminal point of S(4, 9) .

Possible Answers:

<5,5>

<5, -5>

<-5, -5>

<-5, 5>

Correct answer:

<5,5>

Explanation:

To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

$\overrightarrow{RS}=<4-(-1), 9-4>=<5, 5>$

Report an Error

Example Question #1 : Find A Direction Vector When Given Two Points

Find the direction vector that has an initial point at Z(1, 1) and a terminal point at A(4, 8) .

Possible Answers:

<-3, -7>

<3, 7>

<-3, 7>

<7, 3>

Correct answer:

<3, 7>

Explanation:

To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

$\overrightarrow{ZA}=<4-1, 8-1>=<3, 7>$

Report an Error

Example Question #611 : Pre Calculus

Find the direction vector with an initial point of T(-4, 5) and a terminal point B(4, -1) .

Possible Answers:

<-8, 6>

<8, -6>

<-8, 6>

<-6, 8>

Correct answer:

<8, -6>

Explanation:

To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

$\overrightarrow{TB}=<4-(-4), -1-5>=<8, -6>$

Report an Error

Example Question #12 : Find A Direction Vector When Given Two Points

If $\overrightarrow{DE}=<5, -1>$ and E=(-2, -1) , which of the following is a possible point for ?

Possible Answers:

(0, -3)

(-3, -2)

(-7,0)

(3, -2)

Correct answer:

(-7,0)

Explanation:

To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

To find the x-coordinate of ,

-2-x=5

x=-7

To find the y-coordinate of ,

-1-y=-1

y=0

Report an Error

Example Question #11 : Find A Direction Vector When Given Two Points

If $\overrightarrow{EF}=<2, -8>$ and E=(-1, 5) , what is one possible point for ?

Possible Answers:

(1, -3)

(-3, -3)

(3, 3)

(-3, 3)

Correct answer:

(1, -3)

Explanation:

To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

To find the x-coordinate of ,

x-(-1)=2

x=1

To find the y-coordinate of ,

y-5=-8

y=-3

Report an Error

Example Question #12 : Find A Direction Vector When Given Two Points

If $\overrightarrow{OP}=<4, -2>$ and O=(2, 10) , what is a possible value of ?

Possible Answers:

(-6, 8)

(6, -2)

(6, 8)

(8, 6)

Correct answer:

(6, 8)

Explanation:

To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

To find the x-coordinate of ,

x-2=4

x=6

To find the y-coordinate of ,

y-10=-2

y=8

Report an Error

Example Question #1 : Express A Vector In Polar Form

Rewrite the vector $\vec{v}= 3 \hat{i} + 5 \hat{j}$ from Cartesian coordinates to polar coordinates $\vec{v} = \left \langle r \angle \theta \right \rangle$ .

Possible Answers:

$\vec{v} = \left \langle \sqrt{21} \angle 32.64^\circ \right \rangle$

$\vec{v} = \left \langle \sqrt{8} \angle 60^\circ \right \rangle$

$\vec{v} = \left \langle 16 \angle 60^\circ \right \rangle$

$\vec{v} = \left \langle \sqrt{34} \angle 59.04^\circ \right \rangle$

Correct answer:

$\vec{v} = \left \langle \sqrt{34} \angle 59.04^\circ \right \rangle$

Explanation:

To convert to polar form, we need to find the magnitude of the vector, , and the angle it forms with the positive -axis going counterclockwise, or $\theta$ . This is shown in the figure below.

Vecfssec

We find the angle using trigonometric identities:

$\tan{\theta}= \frac{5}{3}$

Using a calculator,

$\theta = \arctan{\frac{5}{3}} \approx 59.04^\circ$

To find the magnitude of a vector, we add up the squares of each component and take the square root:

$r= \left | \vec{v}\right | = \sqrt{3^2+5^2}=\sqrt{34}$ .

So, our vector written in polar form is

$\vec{v} = \left \langle \sqrt{34} \angle 59.04^\circ \right \rangle$

Report an Error

View Pre-Calculus Tutors

Alexander
Certified Tutor

Champlain College, Bachelor of Science, Game and Interactive Media Design.

View Pre-Calculus Tutors

Yosef
Certified Tutor

Cooper Union for the Advancement of Science and Art, Bachelor of Engineering, Mechanical Engineering. Rensselaer Polytechnic ...

View Pre-Calculus Tutors

Manisha
Certified Tutor

CMP homoeopathy Medical college, Bachelor of Science, Human Biology.

All Precalculus Resources

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

Popular Subjects

Statistics Tutors in Washington DC, French Tutors in Chicago, Math Tutors in San Diego, Computer Science Tutors in Atlanta, Biology Tutors in Denver, Reading Tutors in Houston, Physics Tutors in Los Angeles, LSAT Tutors in Chicago, French Tutors in Atlanta, Math Tutors in Chicago

Popular Courses & Classes

GRE Courses & Classes in Chicago, ISEE Courses & Classes in San Diego, Spanish Courses & Classes in Chicago, SSAT Courses & Classes in Atlanta, LSAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Houston, ISEE Courses & Classes in Phoenix, ACT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in New York City, Spanish Courses & Classes in Phoenix

Popular Test Prep

MCAT Test Prep in Seattle, ACT Test Prep in Dallas Fort Worth, GMAT Test Prep in Boston, GMAT Test Prep in Denver, GMAT Test Prep in San Diego, MCAT Test Prep in Chicago, SSAT Test Prep in Atlanta, SSAT Test Prep in Phoenix, SAT Test Prep in Boston, LSAT Test Prep in Phoenix

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 : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Find A Direction Vector When Given Two Points

Example Question #1 : Find A Direction Vector When Given Two Points

Example Question #1 : Find A Direction Vector When Given Two Points

Example Question #1 : Find A Direction Vector When Given Two Points

Example Question #1 : Find A Direction Vector When Given Two Points

Example Question #611 : Pre Calculus

Example Question #12 : Find A Direction Vector When Given Two Points

Example Question #11 : Find A Direction Vector When Given Two Points

Example Question #12 : Find A Direction Vector When Given Two Points

Example Question #1 : Express A Vector In Polar Form

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: