?Let u, v, and w be three-dimensional vectors and c be a real number. Prove the
Chapter 2, Problem 221(choose chapter or problem)
Let u, v, and w be three-dimensional vectors and c be a real number. Prove 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 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
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