IXL - Add vectors (Precalculus practice)

Find the sum

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Learn with an example

question

Find the sum

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 sum of two vectors in component form, add the

-components

and add the

-components.

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 sum

write

and

in component form and add their components.

Afterwards, check your answer using the triangle method of vector addition since the initial point of

is 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 sum

Plug in

⟨

–

⟩

and

⟨

–

⟩

⟨

–

⟩

⟨

–

⟩

Plug in

⟨

–

⟩

and

⟨

–

⟩

Add the components

⟨

–

⟩

Add the components

⟨

–

⟩

So,

⟨

–

⟩

Check your answer using the triangle method of vector addition.

Graph

⟨

–

⟩

starting at the initial point of

⟨

–

⟩

completes the triangle, then your answer is correct.

⟨

–

⟩

completes the triangle, so it is true that

⟨

–

⟩

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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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