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## Homework Statement

Prove that vectors [tex]\vec{u}[/tex], [tex]\vec{v}[/tex]and [tex]\vec{w}[/tex] are coplanar if and only if vectors [tex]\vec{u}[/tex], [tex]\vec{v}[/tex]and [tex]\vec{w}[/tex]are linearly dependent

## Homework Equations

## The Attempt at a Solution

This may sound like an awkward question, but I am having much difficulty proving this. I tried to multiply each vector by a scalar, but got stuck, below is my solution, up until I got stuck.Any help is much appreciated!

We need to write [tex]\vec{u}[/tex]= c

_{1}[tex]\vec{v}[/tex]+ c

_{2}[tex]\vec{w}[/tex]as:

[x

_{1}, y

_{1}, z

_{1}] = c

_{1}[x

_{2}, y

_{2}, z

_{2}] + c

_{2}[x

_{3},y

_{3}, z

_{3}]

[x

_{1}, y

_{1}, z

_{1}] = [c

_{1}x

_{2}, c

_{1}y

_{2}, c

_{1}z

_{2}] + [c

_{2}x

_{3}, c

_{2}y

_{3}, c

_{2}z

_{3}]

x

_{1}= c

_{1}x

_{2}+ c

_{2}x

_{3}

y

_{1}= c

_{1}y

_{2}+ c

_{2}y

_{3}

z

_{1}= c

_{1}z

_{2}+ c

_{2}z

_{3}

This is where I got stuck, and Im not sure what to do next.

Thanks,