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Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

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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 .

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

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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:

<-1, -4>

<-4, 1>

<-4, -1>

<1, 4>

Correct answer:

<-1, -4>

Explanation:

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

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

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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:

<9, 2>

<-9, -2>

<2, 9>

<-2, -9>

Correct answer:

<-9, -2>

Explanation:

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

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

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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.

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

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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:

<7, 3>

<-3, 7>

<3, 7>

<-3, -7>

Correct answer:

<3, 7>

Explanation:

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

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

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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>

<-6, 8>

<-8, 6>

Correct answer:

<8, -6>

Explanation:

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

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

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Example Question #101 : Matrices And Vectors

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

Possible Answers:

(-3, -2)

(3, -2)

(0, -3)

(-7,0)

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

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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

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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

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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:

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

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

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

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

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

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

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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 #101 : Matrices And Vectors

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

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