일반물리학 1 — Vectors: Problem 37

37 Three vectors are given by \(\vec{a} = 3.0\hat{i} + 3.0\hat{j} - 2.0\hat{k}\), \(\vec{b} = -1.0\hat{i} - 4.0\hat{j} + 2.0\hat{k}\), and \(\vec{c} = 2.0\hat{i} + 2.0\hat{j} + 1.0\hat{k}\). Find (a) \(\vec{a} \cdot (\vec{b} \times \vec{c})\), (b) \(\vec{a} \cdot (\vec{b} + \vec{c})\), and (c) \(\vec{a} \times (\vec{b} + \vec{c})\).