Podcast
Play an AI-generated podcast conversation about this lesson
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 $c = 7j - 4k$?
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 $c = 7j - 4k$?
What is the value of $|a \cdot (b \times c)|$ for vectors $a = i + 2j - k$, $b = -2i + 3k$, and $c = 7j - 4k$?
Signup and view all the answers
