__maths__>__Properties of Vector Arithmetics__>__Properties of Cross Product__### Cross Product : Closure Property

In this page, you will learn about the closure property of vector cross product.

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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 cross product of two vectors be another vector in the vector space?

- Yes
- Yes
- No

The answer is 'Yes'. Cross product of two vectors is another vector.

• Cross product of two vectors is another vector - closed.

**Closure Property of Cross Product: ** For any vectors ` vec(a), vec(b) in bbb V`,

` vec(a) xx vec(b) in bbb V`

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