Consider two vectors a and b. (12 pts: 3+3+3+3) (a) define the dot product mathematically in two different ways. (hint: one involving components, one involving lengths/angle.) (b) give a brief physical interpretation of what the dot product means. (give a concrete example if you like.) (c) define the vector cross product mathematically in two different ways. (hint: one involving components, one involving lengths/angle.) (d) give a brief physical interpretation of what the cross product means. (give a concrete example if you like.) extra credit (6 pts) find the angle between the "face diagonal" and "body diagonal" of a cube