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

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