IXL - Linear combinations of three-dimensional vectors (Precalculus practice)

⟨

–

⟩

and

⟨

–

⟩

find

–

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Learn with an example

question

⟨

–

⟩

and

⟨

–

⟩

find

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

(

–

the second component is the change in the

-direction

(

–

and the third component is the change in the

-direction

(

–

To multiply a vector by a scalar, multiply each component by the scalar. To add two vectors, add their components. To subtract two vectors, subtract their components.

solution

Find

Plug in

⟨

–

⟩

and

⟨

–

⟩

⟨

–

⟩

⟨

–

⟩

Plug in

⟨

–

⟩

and

⟨

–

⟩

⟨

–

⟩

⟨

–

⟩

Add the components

⟨

–

⟩

Add the components

⟨

–

⟩

So,

⟨

–

⟩

Looking for more? Try this:

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Z.3Add and subtract three-dimensional vectors

Z.4Scalar multiples of three-dimensional vectors

Y.14Linear combinations of vectors

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