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\noindent {\bf Problem statement} \footnote*{This problem resembles problems in several textbooks.}~Suppose that $
\vec{v}$ is a vector in ${\bf R}^3$ which is not the zero vector.

\medskip

\noindent a) If $\vec{v}\cdot \vec{w} = \vec{v}\cdot\vec{q}$, must it
be true that $ \vec{w}= \vec{q}\thinspace$?

\medskip

\noindent b) If $\vec{v}\times \vec{w} = \vec{v}\times\vec{q}$, must
it be true that $\vec{w}= \vec{q}\thinspace$?

\medskip

\noindent c) If $\vec{v}\cdot \vec{w} = \vec{v}\cdot\vec{q}$ and
$\vec{v}\times \vec{w} =\vec{v}\times\vec{q}$, must it be true that
$\vec{w}= \vec{q}\thinspace$?










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