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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.

Read in the blogs more about the unique learning experience at nubtrek.continue

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



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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`
Dot product of a negative 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`
Dot product of a negative 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`'

                            
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