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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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mathsVector AlgebraProperties of Cross Product

Cross Product : No Multiplicative Inverse

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

click on the content to continue..

What does 'inverse' mean?

• same; identical; similar
• opposite; converse
• 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

|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
• 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.

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

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.

slide-show version coming soon