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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

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