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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
mathsProperties of Vector ArithmeticsProperties of Cross Product

Cross product of a Scalar Multiple

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



click on the content to continue..

Given `vec p = 2i+j-k` and `lambda = 3.1`, what is the scalar multiple `3.1 vec p`?

  • `6.2i+3.1j-3.1k`
  • `6.2i+3.1j-3.1k`
  • `6.2i+j-k`

The answer is '`6.2i+3.1j-3.1k`'

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

  • `lambda(vec p xx vec q)`
  • `|p||lambda q|sin(theta) hat n` if `lambda` is positive
  • `lambda|p||q|sin(theta) hat n`
  • all the above
  • all the above

The answer is 'All the above'

Note that if `lambda` is a negative number, it equals `|p||lambda q|sin(180+theta) hat n`.

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 (lambda vec q)`?

  • `lambda (vec p xx vec q)`
  • `|(i, j, k),(p_x, p_y, p_z),(lambda q_x, lambda q_y, lambda q_z)|`
  • `lambda |(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 scalar multiple of a vector equals scalar multiple of the cross product with the vector.

Cross Product of scalar multiple: For any vectors `vec p, vec q`
`vec p xx (lambda vec q) = lambda (vec p xx vec q)`

Solved Exercise Problem:

Given that `vec p xx vec q = 3j+1.1k`, what is `vec p/(2.1) xx vec q`?

  • `3/(2.1)j+1.1/(2.1)k`
  • `3/(2.1)j+1.1/(2.1)k`
  • `6.3j+2.31k`
  • `3/(2.1)j+1.1k`

The answer is '`3/(2.1)j+1.1/(2.1)k`'.

                            
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