Chapter 12.4, Problem 29E

(a)

To determine

Use dot cross product and dot product notation to describe a vector projection of $u$ onto $v$.

(b)

To determine

Use dot cross product and dot product notation to describe a vector orthogonal to $u$ and $v$.

(c)

To determine

Use dot cross product and dot product notation to describe the vector orthogonal to $u\times v$ and $w$.

(d)

To determine

Use dot cross product and dot product notation to describe the volume of the parallelepiped determined by $u$, $v$, and $w$.

(e)

To determine

Use dot cross product and dot product notation to describe a vector orthogonal to $u\times v$ and $u\times w$.

(f)

To determine

Use dot cross product and dot product notation to describe a vector of length $\left|u\right|$ in the direction of $v$.