IXL - Find the component form of a three-dimensional vector (Precalculus practice)

Write

in component form, with

(

–

)

and

(

–

)

ref_doc_title.

Learn with an example

question

Write

in component form, with

(

–

)

and

(

–

)

key idea

A vector is a quantity that has both a length and a direction. The length of a vector is called the

magnitude,

and it is equal to the distance between the initial (starting) point and terminal (ending) point.

If a vector has the initial point

(

)

and the terminal point

(

)

its component form is:

⟨

–

⟩

The first component is the change in the

-direction

(

–

the second component is the change in the

-direction

(

–

and the third component is the change in the

-direction

(

–

solution

To write

in component form, find the change in the

-direction,

and

-direction

from the initial point

(

–

)

to the terminal point

(

–

)

Find the change in the

-direction.

Subtract the

-coordinate

of the initial point

(

–

)

from the

-coordinate

of the terminal point

(

–

)

The change in the

-direction

is:

–

Find the change in the

-direction.

Subtract the

-coordinate

of the initial point

(

–

)

from the

-coordinate

of the terminal point

(

–

)

The change in the

-direction

is:

–

Find the change in the

-direction.

Subtract the

-coordinate

of the initial point

(

–

)

from the

-coordinate

of the terminal point

(

–

)

The change in the

-direction

is:

–

So, the component form of

⟨

–

⟩

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