Dot product of $$$\left\langle 7, -3\right\rangle$$$ and $$$\left\langle -6, 6\right\rangle$$$

Calculate $$$\left\langle 7, -3\right\rangle\cdot \left\langle -6, 6\right\rangle$$$.

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: $$$\left\langle 7, -3\right\rangle\cdot \left\langle -6, 6\right\rangle = \left(7\right)\cdot \left(-6\right) + \left(-3\right)\cdot \left(6\right) = -60.$$$

$$$\left\langle 7, -3\right\rangle\cdot \left\langle -6, 6\right\rangle = -60$$$A