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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 vector cross product with a null vector.



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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 cross product as
`vec p xx vec q = |vec p||vec q|sin theta hat n`
What is `vec p xx (vec 0)`?

  • null vector
  • null vector
  • `vec p`

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

Given the definition of cross product as
`vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`
What is `vec p xx (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 cross product is `0`.

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

Cross product with null vector: For any vector `vec p in bbb V`
`vec p xx vec 0 = 0`

Solved Exercise Problem:

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

  • unknown
  • `-vec(x)`
  • `-vec(x)`
  • `vec 0`

The answer is '`vec 0`'.

                            
slide-show version coming soon