Dot product of $$$\left\langle 3, -2, -5\right\rangle$$$ and $$$\left\langle -1, -5, 0\right\rangle$$$

Calculate $$$\left\langle 3, -2, -5\right\rangle\cdot \left\langle -1, -5, 0\right\rangle$$$.

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: $$$\left\langle 3, -2, -5\right\rangle\cdot \left\langle -1, -5, 0\right\rangle = \left(3\right)\cdot \left(-1\right) + \left(-2\right)\cdot \left(-5\right) + \left(-5\right)\cdot \left(0\right) = 7.$$$

$$$\left\langle 3, -2, -5\right\rangle\cdot \left\langle -1, -5, 0\right\rangle = 7$$$A