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Precalculus : Algebraic Vectors and Parametric Equations

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Example Questions

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

Find the vector through the points

(12,5) and (-4,22) .

Possible Answers:

<-16,27>

<8,17>

<16,-17>

<8,27>

<16,17>

Correct answer:

<16,-17>

Explanation:

The correct vector is given by the subtraction of the two points: (12,5)-(-4,22) .

Since the subtraction here is component-wise, it is given by the formula: <x_1-x_2,y_1-y_2> .

This results in the vector <16,-17> .

The vector <-16,17> is also correct as it is a scalar multiple of the vector marked as correct, it is found by reversing the order of the subtraction of the two points.

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

Find the vector that has the initial point A(2, -2) and the terminal point B(0, 4) .

Possible Answers:

<-6, -2>

<6, -2>

<-2, 6>

<2, -6>

Correct answer:

<-2, 6>

Explanation:

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

$\overrightarrow{AB}=<0-2, 4-(-2)>=<-2, 6>$

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

Find the direction vector with an initial point of D(-4, -10) and a terminal point C(2, 4) .

Possible Answers:

<-6, -14>

<6, -14>

<6, 14>

<14, 6>

Correct answer:

<6, 14>

Explanation:

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

$\overrightarrow{DC}=<2-(-4), 4-(-10)>=<6, 14>$

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

Find $\overrightarrow{PQ}$ if P=(4, 1) and Q=(-5, 2) .

Possible Answers:

<-9, 1>

<6, 6>

<1, -9>

<9, -1>

Correct answer:

<-9, 1>

Explanation:

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

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

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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:

<3, 7>

<-3, 7>

<7, 3>

<-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 #101 : Matrices And Vectors

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

Possible Answers:

<-6, 8>

<-8, 6>

<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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Precalculus : Algebraic Vectors and Parametric Equations

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 #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 #101 : Matrices And Vectors

All Precalculus Resources

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