Which of the following are always true, and which are not
Chapter 11, Problem 27E(choose chapter or problem)
Which of the following are always true, and which are not always true? Give reasons for your answers.
a. \(|\mathbf{u}|=\sqrt{u \cdot u}\)
b. \(\mathbf{u} \cdot \mathbf{u}=|\mathbf{u}|\)
c. \(\mathbf{u} \times 0=0 \times \mathbf{u}=0\)
d. \(\mathbf{u} \times(-\mathbf{u})=0\)
e. \(\mathbf{u} \times \mathbf{v}=\mathbf{v} \times \mathbf{u}\)
f. \(\mathbf{u} \times(\mathbf{v}+\mathbf{w})=\mathbf{u} \times \mathbf{v}+\mathbf{u} \times \mathbf{w}\)
g. \((\mathbf{u} \times \mathbf{v}) \cdot \mathbf{v}=0\)
h. \((\mathbf{u} \mathbf{v}) \cdot \mathbf{w}=\mathbf{u} \cdot(\mathbf{v} \times \mathbf{w})\)
Equation Transcription:
|𝐮|
𝐮𝐮=|𝐮|
𝐮𝐮
𝐮(-𝐮)
𝐮𝐯=𝐯𝐮
𝐮(𝐯+𝐰)=𝐮𝐯+𝐮𝐰
(𝐮𝐯)𝐯=
(𝐮𝐯)𝐰=𝐮(𝐯𝐰)
Text Transcription:
|u| = sqrt u.u
u.u = |u|
u x0 = 0 x u = 0
u x (-u) = 0
u x v = v x u
u x (v + w) = u x v + u x w
(u x v).v = 0
(u x v).w = u.(v x w)
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