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<item>
  <id>05852076</id>
  <dt>j</dt>
  <an>2011b.00687</an>
  <augroup>
    <au>Maruszewski, Richard F.</au>
  </augroup>
  <ti>When do three planes intersect in a point?</ti>
  <so>Math. Comput. Educ. 44, No. 1, 6-9 (2010).</so>
  <py>2010</py>
  <pu>,</pu>
  <lagroup>
    <la>EN</la>
  </lagroup>
  <ccgroup>
    <cc>G74</cc>
    <cc>G75</cc>
    <cc>I64</cc>
    <cc>I65</cc>
    <cc>H64</cc>
    <cc>H65</cc>
  </ccgroup>
  <utgroup>
    <ut>planes</ut>
    <ut>intersection</ut>
    <ut>geometric solutions</ut>
    <ut>vectors</ut>
    <ut>linear algebra</ut>
  </utgroup>
  <cigroup>
  </cigroup>
  <ligroup>
  </ligroup>
  <abgroup>
    <ab>Summary: We ask the question, ``When do three planes intersect in a point?" The response in a linear algebra class would be that this happens when the three equations are linearly independent. Rather than using this approach, we will attack the problem using a geometric approach and techniques from Calculus III. This presentation of the well-known question is a good example for Calculus III or Linear Algebra classes because it combines many of the concepts in the beginning units on vectors, lines, and planes and can provide some helpful clarity for the students.</ab>
    <rv></rv>
  </abgroup>
</item>