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Thought-Process to Discover Knowledge

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mathsVector AlgebraProperties of Cross Product

cross product of a negative

In this page, you will learn about the vector cross product with the negative of a vector.



click on the content to continue..

Given `vec p = 2i+j-k` what is the negative of `vec p`?

  • `2i+j-k`
  • `-2i-j+k`
  • `-2i-j+k`

The answer is '`-2i-j+k`'

Given the definition of cross product as
`vec p xx vec q = |vec p||vec q|sin theta hat n`
cross product of a negative What is `vec p xx (-vec q)`?

  • `-(vec p xx vec q)`
  • `|p||q|sin(180+theta) hat n`
  • `-|p||q|sin(theta) hat n`
  • all the above
  • all the above

The answer is 'All the above'

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)|`
cross product of a negative What is `vec p xx (-vec q)`?

  • `-(vec p xx vec q)`
  • `|(i, j, k),(p_x, p_y, p_z),(-q_x, -q_y, -q_z)|`
  • `-|(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`
  • all the above
  • all the above

The answer is 'All the above'

 •  Cross product with a negative of a vector is the negative of cross product with the vector.

Cross Product with the negative: For any vectors `vec p, vec q`
`vec p xx (-vec q) = -(vec p xx vec q)`

Solved Exercise Problem:

Given `vec p xx vec q = -3i` what is `(-vec p) xx vec q`?

  • `3i`
  • `3i`
  • `-3i`
  • `i`
  • `3`

The answer is '`3i`'

                            
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