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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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mathsProperties of Vector ArithmeticsProperties of Dot Product

Distributive Property over Vector Addition

In this page, learn about the distributive property of vector dot product over vector addition.

click on the content to continue..

What does 'distributive' mean?distributive property illustration

  • to share; to spread
  • to share; to spread
  • to restrict; to arrest

The answer is 'to share; to spread'

Given the definition of dot product as
`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z`
dot product distributive property over vector addition What is `vec p cdot (vec q+vec r)`

  • `vec p cdot ((q_x+r_x)i+(q_y+r_y)j+(q_z+r_z)k)`
  • `p_x(q_x+r_x)+p_y(q_y+r_y)+p_z(q_z+r_z)`
  • `vec p cdot vec q + vec p cdot vec r`
  • all the above
  • all the above

The answer is 'all the above'.

 •  Dot product of sum of vectors is sum of dot products with the vectors - Distributive.

Distributive Property: For any given vectors `vec p, vec q, vec r in bbb V`
`color(coral)(vec p) cdot (vec q + vec r) = color(coral)(vec p) cdot vec q + color(coral)(vec p) cdot vec r`

Solved Exercise Problem:

If the dot products of two vectors `vec a` and `vec b` with a third vector `vec c` are `2` and `3`, what is `vec c cdot (vec a + vec b)` ?

  • `5`
  • `5`
  • `6`
  • `2/3`
  • `3/2`

Answer is '`5`'.

slide-show version coming soon