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<title>
9.4 - Messing around with the cross product
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<h2>9.4 - Messing around with the cross product</h2>
<p>One problem per group, and eventually we'll share answers...
<ol>
<li>Consider the vector $\myv c=\myv a \times(\myv a \times \myv b)$.  Is $\myv c \perp \myv a$?  Is $\myv c \perp \myv b$?  Either give a reason justifying the truth of the statement, or a counterexample.
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<li>Suppose that $\uv j \times \myv a=\uv i$.  Give two possible solutions, and discuss others.
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<li>Given that $\myv a=\myc{1,2,3}$ and $\myv b=\myc{1,-1,-1}$ sketch the collection of all position vectors $\myv c$ satisfying $\myv a \times \myv b=\myv a \times \myv c$.
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<li>Show that $\myv a$ is perpendicular to $(\myv a - \myv b)\times(\myv a + \myv b)$.
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