Conceptual Questions

Can the magnitude of the displacement vector be more than the distance traveled? Less than the distance traveled? Explain.

If $\vec{C}=\vec{A}+\vec{B}$, can $C=A+B?$ Can $C>A+B?$ For each, show how or explain why not.

If $\vec{C}=\vec{A}+\vec{B}$, can $C=0?$ Can $C<0?$ For each, show how or explain why not.

Is it possible to add a scalar to a vector? If so, demonstrate. If not, explain why not.

How would you define the zero vector $\vec{0}?$

Can a vector have a component equal to zero and still have nonzero magnitude? Explain.

Can a vector have zero magnitude if one of its components is nonzero? Explain.

Suppose two vectors have unequal magnitudes. Can their sum be zero? Explain.

Are the following statements true or false? Explain your answer.

1. The magnitude of a vector can be different in different coordinate systems.

2. The direction of a vector can be different in different coordinate systems.

3. The components of a vector can be different in different coordinate systems.