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Let \(\mathbf{a}\) be a vector of length \(2\), and let \(\mathbf{b}\) and \(\mathbf{c}\) 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, enter a question mark.

 Oct 11, 2021
 #1
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$\mathbf{a}\bullet( \mathbf{b} + \mathbf{c}) = 7$

$\mathbf{b}\bullet(\mathbf{a} +\mathbf{b} + \mathbf{c}) = 8$

$(\mathbf{a} + 2\mathbf{b})\bullet(-3\mathbf{a} + 3\mathbf{c}) = 10$

 Oct 11, 2021

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