?Show that vectors \(\mathbf{u}=\langle 1,0,-8\rangle\) , \(\mathbf{v}=\langle

Chapter 2, Problem 222

(choose chapter or problem)

Show that vectors \(\mathbf{u}=\langle 1,0,-8\rangle\) , \(\mathbf{v}=\langle 0,1,6\rangle\) , and \(\mathbf{w}=\langle-1,9,3\rangle\) satisfy the following properties of the cross product.

a. \(\mathbf{u} \times \mathbf{u}=0\)

b. \(\mathbf{u} \times(\mathbf{v}+\mathbf{w})=(\mathbf{u} \times \mathbf{v})+(\mathbf{u} \times \mathbf{w})\)

c. \(c(\mathbf{u} \times \mathbf{v})=(c \mathbf{u}) \times \mathbf{v}=\mathbf{u} \times(c \mathbf{v})\)

d. \(\mathbf{u} \cdot(\mathbf{u} \times \mathbf{v})=\mathbf{0}\)

Text Transcription:

u = langle 1,0,-8 rangle

v = langle 0,1,6 rangle

w = langle -1,9,3 rangle

u times u = 0

u times (v + w) = (u times v) + (u times w)

c(u times v) = (c u) times v = u times (c v)

u cdot (u times v) = 0