IXL - Find a three-dimensional unit vector (Precalculus practice)

Find the unit vector

with the same direction as

⟨

–

⟩

Simplify any radicals.

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Learn with an example

question

Find the unit vector

with the same direction as

⟨

–

⟩

Simplify any radicals.

key idea

A unit vector has a magnitude of 1.

The magnitude of a vector

⟨

⟩

is:

The product of a scalar

and a vector

is the vector

It has magnitude

where

is the absolute value of

and

is the magnitude of

is positive, then

has the same direction as

is negative, then

has the opposite direction of

solution

Find the magnitude of

⟨

–

⟩

Then, divide

by its magnitude to find

Finally, confirm that

is a unit vector with the same direction as

Find the magnitude of

Plug in

–

and

–

(

–

)

(

–

)

(

–

)

Plug in

–

and

–

Divide

by its magnitude to find

⟨

–

⟩

–

Confirm that

is a unit vector.

–

The magnitude of

is 1, so

is a unit vector. Since

was calculated by multiplying

by the positive scalar

has the same direction as

Looking for more? Try this:

$Confetti$

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Z.1Find the magnitude of a three-dimensional vector

Z.4Scalar multiples of three-dimensional vectors

Y.13Find a unit vector

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