Dot product of $$$\left\langle 4, 7, -13\right\rangle$$$ and $$$\left\langle -3, 2, 1\right\rangle$$$
Your Input
Calculate $$$\left\langle 4, 7, -13\right\rangle\cdot \left\langle -3, 2, 1\right\rangle$$$.
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: $$$\left\langle 4, 7, -13\right\rangle\cdot \left\langle -3, 2, 1\right\rangle = \left(4\right)\cdot \left(-3\right) + \left(7\right)\cdot \left(2\right) + \left(-13\right)\cdot \left(1\right) = -11.$$$
Answer
$$$\left\langle 4, 7, -13\right\rangle\cdot \left\langle -3, 2, 1\right\rangle = -11$$$A