Dot product of $$$\left\langle 7, 0, 5\right\rangle$$$ and $$$\left\langle 1, -3, -4\right\rangle$$$
Your Input
Calculate $$$\left\langle 7, 0, 5\right\rangle\cdot \left\langle 1, -3, -4\right\rangle$$$.
Solution
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: $$$\left\langle 7, 0, 5\right\rangle\cdot \left\langle 1, -3, -4\right\rangle = \left(7\right)\cdot \left(1\right) + \left(0\right)\cdot \left(-3\right) + \left(5\right)\cdot \left(-4\right) = -13.$$$
Answer
$$$\left\langle 7, 0, 5\right\rangle\cdot \left\langle 1, -3, -4\right\rangle = -13$$$A