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Triple Scalar Product Quiz
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Triple Scalar Product Quiz

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@RenownedFuchsia

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Questions and Answers

What is the triple scalar product of vectors a, b, and c?

  • $| (a \cdot c) \times b | = |a \cdot c| |b| |\cos \theta|$
  • $| (a \times b) \cdot c | = |a \times b| |c| |\cos \theta|$ (correct)
  • $| (a \times c) \cdot b | = |a \times c| |b| |\cos \theta|$
  • $| (a \cdot b) \times c | = |a \cdot b| |c| |\cos \theta|$

    • What is the volume of the parallelepiped determined by vectors a, b, and c?

  • $|a \times b| |c| |\cos \theta|$
  • $|a \cdot c| |b| |\cos \theta|$
  • $|a \cdot b| |c| |\cos \theta|$
  • $| (a \times b) \cdot c |$ (correct)

    • Which property holds true for the triple scalar product?

  • $(a \times c) \cdot b = a \cdot (c \times b)$
  • $(a \times b) \cdot c = a \cdot (b \times c)$ (correct)
  • $(a \cdot c) \times b = a \times (c \cdot b)$
  • $(a \cdot b) \times c = a \times (b \cdot c)$

    • What is the value of $a \cdot (b \times c)$ for vectors $a = i + 2j - k$, $b = -2i + 3k$, and $c = 7j - 4k$?

    <p>$1$</p> Signup and view all the answers

    What is the value of $|a \cdot (b \times c)|$ for vectors $a = i + 2j - k$, $b = -2i + 3k$, and $c = 7j - 4k$?

    <p>$1$</p> Signup and view all the answers

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