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# precalculus vectors

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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

$\mathbf{a}\bullet( \mathbf{b} + \mathbf{c}) = 7$
$\mathbf{b}\bullet(\mathbf{a} +\mathbf{b} + \mathbf{c}) = 8$
$(\mathbf{a} + 2\mathbf{b})\bullet(-3\mathbf{a} + 3\mathbf{c}) = 10$