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