Chapter 1, Problem 20P

(a)

To determine

Draw the vector $\overrightarrow{f}$.

(b)

To determine

Calculate the vector $2\overrightarrow{f}$ and sketch the vector $2\overrightarrow{f}$.

(c)

To determine

Compare the magnitude of $2\overrightarrow{f}$ to the magnitude of $\overrightarrow{f}$.

(d)

To determine

Compare the direction of $2\overrightarrow{f}$ to the direction of $\overrightarrow{f}$.

(e)

To determine

Calculate the vector $\overrightarrow{f}/2$ and sketch the vector on the graph, putting its tail at $\langle -3,-6,0\rangle$.

(f)

To determine

Compare the magnitude of $\overrightarrow{f}$ with $\overrightarrow{f}/2$.

(g)

To determine

Compare the direction $\overrightarrow{f}/2$ with $\overrightarrow{f}$.

(h)

To determine

Whether multiplying a vector by a scalar changes the magnitude of the vector.

(i)

To determine

The value of scalar quantity $a$.