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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.continue
mathsVector AlgebraProperties of Dot Product

Dot product with a null vector

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



click on the content to continue..

What is a null vector or zero vector?

  • A vector of magnitude `0`
  • `0i+0j+0k`
  • `vec 0`
  • all the above
  • all the above

The answer is 'All the above'

Given the definition of dot product as
`vec p cdot vec q = |vec p||vec q|cos theta`
What is `vec p cdot (vec 0)`?

  • null vector
  • null vector
  • `vec p`
  • `|vec p|`
  • all the above

The answer is 'Null Vector' As `|vec 0| = 0`, the dot product is `0`.

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 0)`?

  • `vec 0`
  • `vec 0`
  • `vec p`
  • `p_x+p_y+p_z`
  • all the above

The answer is '`vec 0`' As all the x, y, z components of `vec 0` is `0`, the dot product is `0`.

 •  Dot product with a null vector results in a null vector.

Dot product with null vector: For any vector `vec p in bbb V`
`vec p cdot vec 0 = 0`

Solved Exercise Problem:

Given that `vec x` has unknown magnitude and direction. What is the result of `vec 0 cdot vec x`?

  • unknown
  • `0`
  • `0`
  • `vec 0`

The answer is '`0`'.

                            
slide-show version coming soon