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

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Answer 1 · 2017-08-13T12:03:04

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

Suppose we have a vectors:

$bb(vec u) = << a, b, c >>$
$bb(vec v) = <<1, 1, 1 >>$

Please note that $bb(vec v)$ is not a unit vector, it just has unit vector components

Then the dot product is:

$bb(vec u * vec v) = << a, b, c >> bb(*) <<1, 1, 1 >>$

$" " = (a)(1) + (b)(1) + (c)(1)$
$" " = a+b+c$

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