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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 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`
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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