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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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.

Read in the blogs more about the unique learning experience at nubtrek.
mathsProperties of Vector ArithmeticsProperties of Dot Product

### Dot Product: Commutative Property

In this page, you will learn about the commutative property of vector dot product.

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
• different

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

Given the definition of dot product as
vec p cdot vec q = |vec p||vec q|cos theta
What is vec q cdot vec p?

• vec p cdot vec q
• |p||q|cos(theta)
• |p||q|cos(-theta)
• all the above
• all the above

The answer is 'All the above' Note that cos(-theta) = cos(theta).

Given the definition of dot product as
vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z
What is vec q cdot vec p?

• vec p cdot vec q
• q_xp_x+q_yp_y+q_zp_z
• p_xq_x+p_yq_y+p_zq_z
• all the above
• all the above

The answer is 'All the above'

• Vectors can be swapped in dot product - commutative.

Commutative Property of Dot Product: For any vector vec p, vec q in bbb V
vec p cdot vec q =vec q cdot vec p

Solved Exercise Problem:

Given that vec p cdot vec q = 2.1i-1.7j+6k, find the vec q cdot 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' as dot product is commutative.

slide-show version coming soon