Pre-Calculus - Find a Direction Vector When Given Two Points

Find $\overrightarrow{PQ}$ if and .

Explanation

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

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

Find $\overrightarrow{MN}$ if and .

Explanation

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

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

Find the direction vector that has an initial point at and a terminal point at .

Explanation

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

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

Find the direction vector that has an initial point at and a terminal point of .

Explanation

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

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

Find the vector through the points

and .

Explanation

The correct vector is given by the subtraction of the two points: .

Since the subtraction here is component-wise, it is given by the formula: .

This results in the vector .

The vector 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.

Find the direction vector that has an initial point at and a terminal point at .

Explanation

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

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

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

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

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

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

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

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

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.

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

Find the direction vector with an initial point of and an terminal point of .

Explanation

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

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

Find the vector that has the initial point and the terminal point .

Explanation

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

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

Find the direction vector with an initial point of and a terminal point .

Explanation

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

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

Find a Direction Vector When Given Two Points

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