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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 of a negative

In this page, you will learn about the result of vector dot product with the negative of a vector.

click on the content to continue..

Given vec p = 2i+j-k, what is the negative of vec p?

• 2i+j-k
• -2i-j+k
• -2i-j+k

The answer is '-2i-j+k'

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

• -(vec p cdot vec q)
• |p||q|cos(180+theta)
• -|p||q|cos(theta)
• all the above
• all the above

The answer is 'All the above'

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

• -(vec p cdot vec q)
• p_x(-q_x)+p_y(-q_y)+p_z(-q_z)
• -(p_xq_x+p_yq_y+p_zq_z)
• all the above
• all the above

The answer is 'All the above'

•  Dot product with a negative of a vector is the negative of dot product with the vector.

Dot Product with the negative: For any vectors vec p, vec q
vec p cdot (-vec q) = -(vec p cdot vec q)

Solved Exercise Problem:

Given vec p cdot vec q = -3i what is (-vec p) cdot vec q?

• 3i
• 3i
• -3i
• i
• 3

The answer is '3i'

slide-show version coming soon