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True or False? If False, you should come up with a counterexample. If True, can you give a proof?
1.
The zero vector is the only vector of length 0.
True False
2.
If \(\norm {\vec {v}-\vec {w}}=0\), then \(\vec {v}=\vec {w}\).
True False
3.
If \(\vec {v}=-\vec {v}\), then \(\vec {v}=\vec {0}\).
True False
4.
If \(\norm {\vec {v}}=\norm {\vec {w}}\), then \(\vec {v}=\vec {w}\).
True False
5.
If \(\norm {\vec {v}}=\norm {\vec {w}}\), then \(\vec {v}=\pm \vec {w}\).
True False
6.
If \(\vec {v}=t\vec {w}\) for some scalar \(t\), then \(\vec {v}\) and \(\vec {w}\) have the same direction.
True False
7.
If \(\vec {v}\), \(\vec {w}\) and \(\vec {v}+\vec {w}\) are non-zero, and \(\vec {v}\) is parallel to \(\vec {v}+\vec {w}\), then \(\vec {v}\) and \(\vec {w}\) are also parallel.
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