There vectors are given by `veca = 3. 0 hati + 3. 0 hatj - 2 .0hatk, vecb=-1 . 0hati - 4. 0hatj + 2.0hatk and vecc=2.0hati + 2.0hatj + 1.0hatk.` Find (a) `veca (vecbxx vecc), (b) veca.(vecb+vecc), and © veca xx (vecb + vecc).`

Explanation

To solve the given problem step by step, we need to find three different vector operations involving vectors **a**, **b**, and **c**. The vectors are defined as follows:

- **Vector a**: \( \vec{a} = 3.0 \hat{i} + 3.0 \hat{j} - 2.0 \hat{k} \)
- **Vector b**: \( \vec{b} = -1.0 \hat{i} - 4.0 \hat{j} + 2.0 \hat{k} \)
- **Vector c**: \( \vec{c} = 2.0 \hat{i} + 2.0 \hat{j} + 1.0 \hat{k} \)

We need to find:
(a) \( \vec{a} \cdot (\vec{b} \times \vec{c}) \)
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