# Dot product of $\left\langle 1, 3, 4\right\rangle$ and $\left\langle 2, 5, 7\right\rangle$

The calculator will find the dot product of two vectors $\left\langle 1, 3, 4\right\rangle$ and $\left\langle 2, 5, 7\right\rangle$, with steps shown.
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$\langle$ $\rangle$
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Calculate $\left\langle 1, 3, 4\right\rangle\cdot \left\langle 2, 5, 7\right\rangle$.
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: $\left\langle 1, 3, 4\right\rangle\cdot \left\langle 2, 5, 7\right\rangle = \left(1\right)\cdot \left(2\right) + \left(3\right)\cdot \left(5\right) + \left(4\right)\cdot \left(7\right) = 45.$
$\left\langle 1, 3, 4\right\rangle\cdot \left\langle 2, 5, 7\right\rangle = 45$A