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\LARGE 

{\hspace{50mm}Quiz 2
\hspace{50mm}Name:\hspace{20mm}}


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Directions:  Answer each question to the best of your ability.  You may use a calculator, but show all work to earn partial credit.  The value of each question follows the question. 

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\begin{enumerate}
\item Let $\vec{u}=2\vec{i}+3\vec{j}+\vec{k}$, $\vec{v}=-\vec{i}+2\vec{j}-3\vec{k}$, and $\vec{w}=2\vec{i}-\vec{j}-\vec{k}$.  For each pair of vectors determine whether the angle between them is less than, equal to, or greater than 90 degrees by calculating the dot products. (3 pts each)

$$\vec{u}*\vec{v}\hspace{60mm}\vec{w}*\vec{v}\hspace{60mm}\vec{u}*\vec{w}$$
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\item For which value(s) of $\lambda$ makes the following 2 vectors perpendicular: $\vec{u}=\lambda\vec{i}+3\vec{j}+\vec{k}$, and $\vec{v}=\lambda\vec{i}+2\vec{j}-7\lambda\vec{k}$ (4 pts)
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\item Calculate the projection of $\vec{v}$ onto $\vec{u}$ if $\vec{u}=2\vec{i}+2\vec{j}+\vec{k}$, and $\vec{v}=-\vec{i}+2\vec{j}-3\vec{k}$.  (4 pts)
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\item Calculate $\vec{u}\,\mathtt{x}\,\vec{v}$.  (4 pts)
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\item Calculate the equation of the plane containing the points (0,-2,2), (1,0,1), and (2,6,4)  (4 pts)
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