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## Homework Statement

Show that if [itex]c=\alpha{a}+\beta{b}[/itex], where [itex]a[/itex] and [itex]b[/itex] are arbitrary vectors and [itex]\alpha[/itex] and [itex]\beta[/itex] are arbitrary scalars, then [itex]c[/itex] is coplanar with [itex]a[/itex] and [itex]b[/itex].

## Homework Equations

Triple scalar product: [itex](a\cdot{b})\times{c}=0[/itex]

## The Attempt at a Solution

[itex]0=a\times(\alpha{a}+\beta{b})\cdot{b}[/itex]

[itex]0=(\alpha{a\times{a}}+\beta{a\times{b}})\cdot{b}[/itex]

[itex]0=\beta({a\times{b}})\cdot{b}[/itex]

[itex]0=({a\times{b}})\cdot{b}[/itex]

[itex]0=({b\times{b}})\cdot{a}[/itex]

Is this right?

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