# What is the dot product of 5i and 8j?

Dec 13, 2016

$0$

#### Explanation:

A property of the scaler (or dot) product is that it is zero if the vectors are perpendicular which $5 \underline{\hat{i}}$ and $8 \underline{\hat{j}}$ clearly are, so without any calculation we know the answer is zero.

We can show this if required:

Let $\vec{u} = 5 \underline{\hat{i}} + 0 \underline{\hat{j}} = \left(\begin{matrix}5 \\ 0\end{matrix}\right)$
and $\vec{v} = 0 \underline{\hat{i}} + 8 \underline{\hat{j}} = \left(\begin{matrix}0 \\ 8\end{matrix}\right)$

The scaler product is:

$\vec{u} \cdot \vec{v} = \left(\begin{matrix}5 \\ 0\end{matrix}\right) \cdot \left(\begin{matrix}0 \\ 8\end{matrix}\right)$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = \left(5\right) \left(0\right) + \left(0\right) \left(8\right)$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = 0 + 0$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = 0$