IXL - Subtract vectors (Precalculus practice)

Find the difference

–

ref_doc_title.

Learn with an example

question

Find the difference

–

key idea

If a vector has the initial point

(

)

and the terminal point

(

)

its component form is:

⟨

–

⟩

The first component,

–

is the change in the

-direction

(horizontal change) and the second component,

–

is the change in the

-direction

(vertical change).

To write the difference of two vectors in component form, subtract the

-components

and subtract the

-components.

Alternatively, the difference of two vectors

–

can be written as the sum

(

–

)

The vector

(

–

)

has the same length as

but points in the opposite direction.

Triangle method of vector addition

If the initial point of one vector is the terminal point of another, then their vector sum completes the triangle.

solution

To find the difference

–

write

and

in component form and subtract their components.

Afterwards, check your answer using the triangle method of vector addition by writing the difference

–

as the sum

(

–

)

and placing the initial point of

(

–

)

at the terminal point of

Write

in component form.

Its initial point is

(

)

(

)

and its terminal point is

(

)

(

–

)

Component form

⟨

–

⟩

Component form

Plug in

–

and

⟨

–

⟩

Plug in

–

and

⟨

–

⟩

Write

in component form.

Its initial point is

(

)

(

–

)

and its terminal point is

(

)

(

–

)

Component form

⟨

–

⟩

Component form

Plug in

–

and

⟨

–

⟩

Plug in

–

and

⟨

–

⟩

Find the difference

–

Plug in

⟨

–

⟩

and

⟨

–

⟩

⟨

–

⟩

–

⟨

–

⟩

Plug in

⟨

–

⟩

and

⟨

–

⟩

Subtract the components

⟨

–

⟩

Subtract the components

⟨

⟩

So,

–

⟨

⟩

Check your answer using the triangle method of vector addition.

Write the difference

–

as the sum

(

–

)

and place the initial point of

–

at the terminal point of

Graph

(

–

)

⟨

⟩

starting at the shared initial point

(

)

⟨

⟩

is a diagonal of the parallelogram formed by

and

–

then your answer is correct.

⟨

⟩

completes the triangle, so it is true that

–

⟨

⟩

Looking for more? Try this:

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Y.2Find the component form of a vector

Y.5Graph a resultant vector using the triangle method

A.4Add and subtract integers

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