Given: A = 3i + 4j + 2k, B = 2i − j + 5k. Calculate A - B and A x B

The dot product is calculated by multiplying corresponding components and summing the results.

$$A \cdot B = (3)(2) + (4)(-1) + (2)(5)$$ $$A \cdot B = 6 - 4 + 10$$ $$A \cdot B = 2 + 10$$ $$A \cdot B = \boxed{12}$$

The cross product can be calculated using the determinant of a matrix:

$$A \times B = \begin{vmatrix} i & j & k \\ 3 & 4 & 2 \\ 2 & -1 & 5 \end{vmatrix}$$ $$A \times B = i((4)(5) - (2)(-1)) - j((3)(5) - (2)(2)) + k((3)(-1) - (4)(2))$$ $$A \times B = i(20 - (-2)) - j(15 - 4) + k(-3 - 8)$$ $$A \times B = i(20 + 2) - j(11) + k(-11)$$ $$A \times B = \boxed{22i - 11j - 11k}$$