# Dot product of $\left\langle - 6 t, 2, 6 t^{2}\right\rangle$ and $\left\langle 0, 6, 0\right\rangle$

The calculator will find the dot product of two vectors $\left\langle - 6 t, 2, 6 t^{2}\right\rangle$ and $\left\langle 0, 6, 0\right\rangle$, with steps shown.
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Calculate $\left\langle - 6 t, 2, 6 t^{2}\right\rangle\cdot \left\langle 0, 6, 0\right\rangle$.
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: $\left\langle - 6 t, 2, 6 t^{2}\right\rangle\cdot \left\langle 0, 6, 0\right\rangle = \left(- 6 t\right)\cdot \left(0\right) + \left(2\right)\cdot \left(6\right) + \left(6 t^{2}\right)\cdot \left(0\right) = 12.$
$\left\langle - 6 t, 2, 6 t^{2}\right\rangle\cdot \left\langle 0, 6, 0\right\rangle = 12$A