IXL - Find the magnitude of a vector (Precalculus practice)

Find the magnitude of the vector. Write your answer in simplified form.

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question

Find the magnitude of the vector. Write your answer in simplified form.

key idea

A vector has length and direction. The length is called the

magnitude,

and equals the distance between the initial (starting) point and terminal (ending) point.

is a vector with initial point

(

)

and terminal point

(

)

Its magnitude is the distance between

and

which is 10. The arrow head at

shows its direction.

The distance between the two points

(

)

and

(

)

is given by the distance

formula.

(

–

)

(

–

)

solution

To find the magnitude of the vector, first locate its initial point at the base of the arrow and its terminal point at the tip of the arrow.

Its initial point is

(

)

and its terminal point is

(

)

Since the

-coordinates

of the initial point

(

)

and terminal point

(

)

are the same, the vector is vertical. So, the magnitude is the absolute value of the difference of the

-coordinates,

which is

–

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B.13Distance formula

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