In this page, you will learn that the vector dot product is not closed.

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What does 'closure' mean?

- closed
- not open
- both the above
- both the above

Answer is 'both the above'

What does "span" mean?

- Full extent of something; all that is included in that;
- Full extent of something; all that is included in that;
- past tense of spin

The answer is 'Full extent of something'

What is the span of vectors in 3D coordinate system?

- `ai+bj+ck` with `a,b,c in RR`
- the components of vector taking any real number
- `RR^3`
- all the above
- all the above

The answer is 'All the above'

Vector space `bbb V` consists of all the vectors with real numbers as components.

Is dot product of two vectors another vector in the vector space?

- Yes
- No
- No

The answer is 'No'. Dot product of two vectors is a scalar real number.

• Dot product of two vectors is a scalar and not a vector - not closed.

**Dot Product is Not Closed: ** For any vectors ` vec(a), vec(b) in bbb V`,

` vec(a)cdot vec(b) !in bbb V`

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