Let "a" be a vector of length 2, and let "b" and "c" be vectors such that \(\mathbf{a} \bullet \mathbf{b} = 3, \mathbf{a} \bullet \mathbf{c} = 4, \mathbf{b} \bullet \mathbf{c} = 5.\)
Enter in the numbers \(\mathbf{a}\bullet( \mathbf{b} + \mathbf{c}), \mathbf{b}\bullet(\mathbf{a} +\mathbf{b} + \mathbf{c}), (\mathbf{a} + 2\mathbf{b})\bullet(-3\mathbf{a} + 3\mathbf{c})\)
below, in the order listed above. If any of these cannot be uniquely determined from the information given, answer with a question mark.
I would really appreciate an explanation as well as an answer, thank you!
