Question

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

Answer 1

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:

`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`