Solution

 

b)

$$\begin{align*} A\times B &= \begin{vmatrix} a_x & a_y & a_z\\ 10 & -6 & 8\\ 1 & 0 & 2\\ \end{vmatrix}\\ \\ A\times B &= -12a_x + 8a_y - (-6a_z + 20a_y)\\ \\ A\times B &= -12a_x -12a_y + 6a_z\\ \\ &\boxed{A\times B = (-12, -12, 6)} \end{align*}$$

c)

$$\begin{align*} 2A- 3B &= 2A + (-3B) \\ \\ 2A- 3B &= 2\cdot (10,-6, 8) + (-3)\cdot (1,0,2)\\ \\ 2A- 3B &= (20,-12, 16) + (-3, 0, -6)\\ \\ &\boxed{2A- 3B = (17, -12, 10)} \end{align*}$$

Answer