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Title: Cross Product
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Series: Linear Algebra
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Chapter: Vectors in $ \mathbb{R}^n $
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YouTube-Title: Linear Algebra 10 | Cross Product
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Bright video: https://youtu.be/HZM7K6MEdDU
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Dark video: https://youtu.be/sa8REnW-p8o
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Ad-free video: Watch Vimeo video
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Exercise Download PDF sheets
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: la10_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $\mathbf{v},\mathbf{w} \in \mathbb{R}^3$ be given by $\mathbf{v} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}$ and $\mathbf{w} = \begin{pmatrix} -2 \ 1 \ 0 \end{pmatrix}$. What is the cross product $\mathbf{v} \times \mathbf{w}$?
A1: $0$
A2: $\begin{pmatrix} -1 \ 1 \ 0 \end{pmatrix}$
A3: $\begin{pmatrix} -3 \ 6 \ 6 \end{pmatrix}$
A4: $\begin{pmatrix} -3 \ -6 \ 5 \end{pmatrix}$
Q2: Let $\mathbf{e}_1, \mathbf{e}_2, \mathbf{e}_3 \in \mathbb{R}^3$ be the canonical unit vectors. What is not correct?
A1: $ \mathbf{e}_1 \times \mathbf{e}_3 = \mathbf{e}_2$
A2: $ \mathbf{e}_1 \times \mathbf{e}_2 = \mathbf{e}_3$
A3: $ \mathbf{e}_2 \times \mathbf{e}_3 = \mathbf{e}_1$
A4: $ \mathbf{e}_3 \times \mathbf{e}_1 = \mathbf{e}_2$
A5: $ \mathbf{e}_3 \times \mathbf{e}_2 = -\mathbf{e}_1$
Q3: What is not a property of the cross product $ \times: \mathbb{R}^3 \times \mathbb{R}^3 \rightarrow \mathbb{R}^3$?
A1: $\mathbf{u} \times \mathbf{v} = \mathbf{v} \times \mathbf{u}$ for all $\mathbf{u}, \mathbf{v} \in \mathbb{R}^3$.
A2: $\mathbf{u} \times \mathbf{v} = - \mathbf{v} \times \mathbf{u}$ for all $\mathbf{u}, \mathbf{v} \in \mathbb{R}^3$.
A3: $\mathbf{u} \times \mathbf{u} = \mathbf{0}$ for all $\mathbf{u} \in \mathbb{R}^3$.
A4: $\mathbf{u} \times \mathbf{0} = \mathbf{0}$ for all $\mathbf{u} \in \mathbb{R}^3$.
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Last update: 2024-10
