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Thought-Process to Discover Knowledge

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summary of this topic

Properties of Cross Product

Properties of Cross Product

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 »  vector cross product does not have multiplicative inverse

Cross Product : No Multiplicative Inverse

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Cross product is not invertible - No multiplicative inverse and no definition of division.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, learn that the cross product does not have a multiplicative inverse.


Keep tapping on the content to continue learning.
Starting on learning that the cross product does not have a multiplicative inverse.

What does 'inverse' mean?

  • same; identical; similar
  • opposite; converse

The answer is 'opposite; converse'.

For two vectors `vec p` and `vec q`, the vector cross product is given by multiplication of
 •  magnitude of one vector and
 •  the magnitude of the component of second vector in perpendicular to the first vector

vector cross product illustration
`|vec p xx vec q| = |p| |b| `
where `|b|` is the component of `vec q` in perpendicular to `vec p`.

Given `vec p xx vec q` and `vec p` can `vec q` be calculated?

What is division?

  • inverse of multiplication
  • does not have any relation to multiplication

The answer is 'inverse of multiplication'.

Since cross product is not invertible, the inverse of cross product -- a division -- is not defined.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Cross Product - No Multiplicative Inverse: For any vector `vec p, vec q in bbb V`; it is not possible to calculate `vec q` using the values `vec p` and `vec p xx vec q`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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Progress

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Progress

What does 'inverse' mean?
same;identical;similar
same; identical; similar
opposite;converse
opposite; converse
The answer is 'opposite; converse'.
For two vectors p and q, the vector cross product is given by multiplication of magnitude of one vector and the magnitude of the component of second vector in perpendicular to the first vector. ;; magnitude vector p cross vector q = magnitude p magnitude b ; where magnitude b is the component of vector q in perpendicular to vector p. Given vector p cross vector q and vector p can vector q be calculated?
What is division?
inverse
inverse of multiplication
does;not;have;any;relation
does not have any relation to multiplication
The answer is 'inverse of multiplication'.
Since cross product is not invertible, the inverse of cross product -- a division -- is not defined.
Cross product is not invertible - No multiplicative inverse and no definition of division.
Cross Product - No Multiplicative Inverse: For any vector p, q, in vector space V, it is not possible to calculate vector q using the values vector p and vector p cross vector q.

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