Chapter 7

Describe geometrically all points in 3-space whose coordinates satisfy the given condition(s). $$ 1 \leq x^{2}+y^{2}+z^{2} \leq 9, z \leq 0 $$

Describe the surface in 3 space defined by the given set of points. $$ \left\\{(x, y, z) \mid x^{2}+y^{2}=1\right\\} $$

Describe the surface in 3 space defined by the given set of points. $$ \left\\{(x, y, z) \mid z=1-y^{2}\right\\} $$

Determine whether the cross product (6) of two vectors is commutative. That is, does \(\mathbf{u} \times \mathbf{v}=\mathbf{v} \times\) \(\mathbf{u} ?\)