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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.

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mathsVector AlgebraProperties of Cross Product

Cross product with a null vector

In this page, you will learn about vector cross 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 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`'.

                            
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