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Dot product of $$$\left\langle 1, 1, 2\right\rangle$$$ and $$$\left\langle -2, 3, 1\right\rangle$$$
Your Input
Calculate $$$\left\langle 1, 1, 2\right\rangle\cdot \left\langle -2, 3, 1\right\rangle$$$.
Solution
The dot product is given by $$$\mathbf{\vec{u}}\cdot \mathbf{\vec{v}} = \sum_{i=1}^{n} u_{i} v_{i}$$$.
Thus, what we need to do is multiply the corresponding coordinates and then add up the results: $$$\left\langle 1, 1, 2\right\rangle\cdot \left\langle -2, 3, 1\right\rangle = \left(1\right)\cdot \left(-2\right) + \left(1\right)\cdot \left(3\right) + \left(2\right)\cdot \left(1\right) = 3.$$$
Answer
$$$\left\langle 1, 1, 2\right\rangle\cdot \left\langle -2, 3, 1\right\rangle = 3$$$A