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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 : Not Commutative

In this page, you will learn that the vector cross product is not commutative.

click on the content to continue..

What does 'commute' mean?

• to go to and fro on a regular basis
• to go to and fro on a regular basis
• it does not mean anything

The answer is 'to go to and fro between two places on a regular basis'.

Given the definition of cross product as
vec p xx vec q = |vec p||vec q|sin theta hat n
What is vec q xx vec p?

• vec p xx vec q
• |p||q|sin(theta) hat n
• |p||q|sin(-theta) hat n
• |p||q|sin(-theta) hat n
• all the above

The answer is '|p||q|sin(-theta) hat n'. The angle traversed from vec q to vec p is -theta.

Given the definition of cross product as
vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|
What is vec q xx vec p?

• -vec p xx vec q
• |(i, j, k),(q_x, q_y, q_z),(p_x, p_y, p_z)|
• -|(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|
• all the above
• all the above

The answer is 'All the above'

•  In a cross product if the vectors are swapped, the result is negative of the product. - not commutative.

Not Commutative: For any vector vec p, vec q in bbb V
vec p xx vec q = - vec q xx vec p

Solved Exercise Problem:

Given that vec p xx vec q = 2.1i-1.7j+6k, find the vec q xx vec p.

• -2.1i+1.7j-6k
• -2.1i+1.7j-6k
• 2.1i-1.7j+6k
• sqrt(2.1^2+1.7^2+6^2)
• 2.1^2+1.7^2+6^2

The answer is '-2.1i+1.7j-6k'.

slide-show version coming soon