(Solved): Let i^ be directed to the east, j^ be directed to the north, and k^ be directed upward. What are ...

Let $\hat{i}$ be directed to the east, $\hat{j}$ be directed to the north, and $\hat{k}$ be directed upward. What are the values of products (a) $\hat{i}\cdot \hat{k}$, (b) $(-\hat{k})\cdot (-\hat{j})$, and (c) $\hat{j}\cdot (-\hat{j})$ ? What are the directions (such as east or down) of products (d) $\hat{k}\times \hat{j}$, (e) $(-\hat{i})\times (-\hat{j})$, and (f) $(-\hat{k})\times (-\hat{j})$ ? Note that $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors. (a) (b) (c) (d) (e) (f)