# What is the dot product of <3,4,1 > and <5,-1,2 >?

Dec 19, 2015

13

#### Explanation:

1. Dot product is distributive.
(e.g. $a \cdot \left(b + c\right) = a \cdot b + a \cdot c$)

2. Dot product of 2 vectors that are perpendicular is zero
(e.g. $\hat{i} \setminus \cdot \hat{j} = 0$)

$\left(3 \hat{i} + 4 \hat{j} + \hat{k}\right) \setminus \cdot \left(5 \hat{i} - \hat{j} + 2 \hat{k}\right)$

$= \left(3 \hat{i}\right) \setminus \cdot \left(5 \hat{i}\right) + \left(3 \hat{i}\right) \setminus \cdot \left(- \hat{j}\right) + \left(3 \hat{i}\right) \setminus \cdot \left(2 \hat{k}\right)$

$\textcolor{w h i t e}{s} + \left(4 \hat{j}\right) \setminus \cdot \left(5 \hat{i}\right) + \left(4 \hat{j}\right) \setminus \cdot \left(- \hat{j}\right) + \left(4 \hat{j}\right) \setminus \cdot \left(2 \hat{k}\right)$

$\textcolor{w h i t e}{s} + \left(\hat{k}\right) \setminus \cdot \left(5 \hat{i}\right) + \left(\hat{k}\right) \setminus \cdot \left(- \hat{j}\right) + \left(\hat{k}\right) \setminus \cdot \left(2 \hat{k}\right)$

$= 15 + 0 + 0$

$\textcolor{w h i t e}{s} + 0 - 4 + 0$

$\textcolor{w h i t e}{s} + 0 + 0 + 2$

$= 13$