Activity 9.5.5

In this activity, we are focused on the type of objects being used and whether the expression makes sense to do at all. We are not going to worry about interpreting or understanding what is being measured by these expressions.

1. For each of the expressions below, state whether the result is a scalar, a vector, or undefined. You should write a sentence or two about each to explain your reasoning. (Assume that vectors are nonzero and not orthogonal.)

   1. $\frac{\vv}{\vw}$
   2. $\frac{\vv}{\vw\cdot\vv}$
   3. $(\vu\times\vw)+\vv$
   4. $k(\vu\cdot\vw)+c\vv$
   5. $k(\vu\cdot\vv)\cdot\vw$
   6. $\frac{\vv}{\vecmag{\vw}}$
   7. $(k+\vu)\times \vv$
   8. $k+(\vu\times \vv)$
   9. $\vv+(\vu\cdot \vw)$
   10. $k+\vecmag{\vu\times \vw}$

2. Use the operations of dot product and vector subtraction to write an expression involving $\vu$, $\vv$, and $\vw$ that evaluates to a scalar. You can use other operations if you want.

3. Use the operations of cross product, scalar multiplication, and vector addition to write an expression involving $\vu$, $\vv$, and $\vw$ that evaluates to a vector. You can use other operations if you want.

4. Use the operations of dot product and vector addition to write an expression involving $\vu$, $\vv$, and $\vw$ that is undefined. You can use other operations if you want.