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Precalculus : Find a Direction Vector When Given Two Points

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

Find the directional vector of $\underset{BA}{\rightarrow}$ if points A and B are (2,3) and (-3,2) , respectively.

Possible Answers:

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

$\left \langle \sqrt{13},\sqrt{13}\right \rangle$

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

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

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

Correct answer:

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

Explanation:

To find vector $\underset{BA}{\rightarrow}$ , the point A is the terminal point and point B is the starting point.

The directional vector can be determined by subtracting the start from the terminal point.

$\left \langle \underset{BA}\rightarrow \right \rangle=(2,3)-(-3,2)=\left \langle 5,1\right \rangle$

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Example Question #2 : Find A Direction Vector When Given Two Points

Find the vector through the points

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

Possible Answers:

<8,27>

<16,17>

<-16,27>

<8,17>

<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:

<2, -6>

<-2, 6>

<6, -2>

<-6, -2>

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 #4 : 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:

<14, 6>

<-6, -14>

<6, 14>

<6, -14>

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 #5 : Find A Direction Vector When Given Two Points

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

Possible Answers:

<9, -1>

<1, -9>

<6, 6>

<-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 #6 : Find A Direction Vector When Given Two Points

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

Possible Answers:

<1, -4>

<4, -1>

<-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 #7 : 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:

<2, 9>

<9, 2>

<-9, -2>

<-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 #10 : 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>

<7, 3>

<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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Precalculus : Find a Direction Vector When Given Two Points

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