Are the following statements true or false?

? True False  1. If $\vec{v}$ and $\vec{w}$ are any two vectors, then $||\vec{v} + \vec{w}|| = ||\vec{v}|| + ||\vec{w}||$.

? True False  2. For any scalar $c$ and any vector $\vec{v}$, we have $||c\vec{v}|| = c ||\vec{v}||$.

? True False  3. $(\vec{i} \times \vec{j}) \cdot \vec{k} = \vec{i} \cdot (\vec{j} \times \vec{k})$.

? True False  4. The value of $\vec{v} \cdot (\vec{v} \times \vec{w})$ is always zero.