Dot Product Calculator

Calculate $$$\left\langle 7, 0, -2\right\rangle\cdot \left\langle 1, -1, 4\right\rangle$$$.

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: $$$\left\langle 7, 0, -2\right\rangle\cdot \left\langle 1, -1, 4\right\rangle = \left(7\right)\cdot \left(1\right) + \left(0\right)\cdot \left(-1\right) + \left(-2\right)\cdot \left(4\right) = -1.$$$

$$$\left\langle 7, 0, -2\right\rangle\cdot \left\langle 1, -1, 4\right\rangle = -1$$$A