Dot product of $$$\left\langle 1, 1, 3\right\rangle$$$ and $$$\left\langle 0, 3, 4\right\rangle$$$
Your Input
Calculate $$$\left\langle 1, 1, 3\right\rangle\cdot \left\langle 0, 3, 4\right\rangle$$$.
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: $$$\left\langle 1, 1, 3\right\rangle\cdot \left\langle 0, 3, 4\right\rangle = \left(1\right)\cdot \left(0\right) + \left(1\right)\cdot \left(3\right) + \left(3\right)\cdot \left(4\right) = 15.$$$
Answer
$$$\left\langle 1, 1, 3\right\rangle\cdot \left\langle 0, 3, 4\right\rangle = 15$$$A