# What is the dot product of a vector and <<1, 1, 1 >>?

Aug 13, 2017

The dot product of a first vector with a second vector comprising of unit vector is the sum of the components of the first vector

#### Explanation:

Suppose we have a vectors:

$\boldsymbol{\vec{u}} = \left\langlea , b , c\right\rangle$
$\boldsymbol{\vec{v}} = \left\langle1 , 1 , 1\right\rangle$

Please note that $\boldsymbol{\vec{v}}$ is not a unit vector, it just has unit vector components

Then the dot product is:

$\boldsymbol{\vec{u} \cdot \vec{v}} = \left\langlea , b , c\right\rangle \boldsymbol{\cdot} \left\langle1 , 1 , 1\right\rangle$

$\text{ } = \left(a\right) \left(1\right) + \left(b\right) \left(1\right) + \left(c\right) \left(1\right)$
$\text{ } = a + b + c$