Solved: Which of the following are always true, and which
Chapter 11, Problem 28E(choose chapter or problem)
Which of the following are always true, and which are not always true? Give reasons for your answers.
a. \(\mathbf{u} \cdot \mathbf{v}=\mathbf{v} \cdot \mathbf{u}\)
b. \(\mathbf{u} \times \mathbf{v}=-(\mathbf{v} \times \mathbf{u})\)
c. \((-\mathbf{u}) \times \mathbf{v}=-(\mathbf{u} \times \mathbf{v})\)
d. \((c \mathbf{u}) \cdot \mathbf{v}=\mathbf{u} \cdot(c \mathbf{v})=(\mathbf{u} \cdot \mathbf{v}) \text { (any number } c)\)
e. \(c(\mathbf{u} \times \mathbf{v})=(c \mathbf{u}) \times \mathbf{v}=\mathbf{u} \times(c \mathbf{v})(\text { any number } c)\)
f. \(\mathbf{u} \cdot \mathbf{u}=|\mathbf{u}|^{2}\)
g. \((\mathbf{u} \times \mathbf{u}) \cdot \mathbf{u}=0\)
h. \((\mathbf{u} \times \mathbf{v}) \cdot \mathbf{u}=\mathbf{v} \cdot(\mathbf{u} \times \mathbf{v})\)
Equation Transcription:
𝐮𝐯=𝐯𝐮
𝐮𝐯=-(𝐯𝐮)
(-𝐮)𝐯=-(𝐮𝐯)
(𝐮)𝐯=𝐮(𝐯)=(𝐮𝐯) (any number )
(𝐮𝐯)=(𝐮)𝐯=𝐮(𝐯) (any number )
𝐮𝐮=𝐮
(𝐮𝐮)𝐮=0
(𝐮𝐯)𝐮=𝐯(𝐮𝐯)
Text Transcription:
u . v = v . u
u x v = -(v u)
(-u)x v = -(u x v)
(cu) .v = u . (cv) = c(u . v) (any number c)
c(u x v) = (cu)x v = u x (cv) (any number c)
u . u = |u|^2
(u x u). u = 0
(u x v). u = v ( u x v)
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer