Question

What is the identity of the dot product?
I.E. What is the vector \(\mathbf b\) such that: \[
\mathbf a \cdot \mathbf b = \mathbf a
\]Try to think out of the box on this one!

Answer 1

let b = 1?

Answer 2

Interesting idea! Though \(1\) is not a vector technically.

Answer 3

thats's just normal math , this is vectors

Answer 4

I'm aware of vectors....I'm also aware of the vectors that appear in elementary linear algebra..I thought it was one of those problems that require those 8 rules.

Answer 5

The actual answer is that no such vector exists, but think about what you could do to stretch the definition of vectors to get it to work.

Answer 6

Dude , r u a professor or something @wio

Answer 7

is this a proof question?

Answer 8

Nope, not a proof, it's sort of a trick question.

Answer 9

Let's do a couple of examples. Most things derived in math are done by doing a few examples and noticing a pattern. Some things you don't need to do that, but more likely, you will need some basic examples. Ok?

Answer 10

The only thing is that this question is a bit vague.

Answer 11

Okay, let's say: \[
\mathbf a=a_1\mathbf i+a_2\mathbf j
\]

Answer 12

Do same thing for b.

Answer 13

\[
a_1b_1+a_2b_2=a_1\mathbf i+a_2\mathbf j
\]

Answer 14

a.b is not a vector at al, it won't give a vector, it will give a scalar

Answer 15

yes, your example won't work.

Answer 16

I want to see @wio "stretch" a definition in mathematics, in order to make something exist, that doesnt. ;) lol

Answer 17

@hartnn is right , dot products give scalars