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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
mathsVector AlgebraProperties of Cross Product

Cross Product of Collinear Vectors

In this page, you will learn about the vector cross product between two collinear vectors.



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When two vectors are called 'collinear' vectors?collinear vectors `color(coral)(text(co)) + color(deepskyblue)(text(linear))` means `color(coral)(text(together))+color(deepskyblue)(text(on a line))`

  • the angle between vectors `0^@`
  • the angle between vectors `180^@`
  • the vectors are parallel
  • 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`
cross product of collinear vectors What is `vec p xx vec q`, if the given vectors are collinear?

  • `|p||q|sin 0 hat n`
  • `|p||q|sin 180 hat n`
  • `0`
  • `0`
  • all the above

The answer is 'all the above'. The angle between Collinear vectors can be either `0^@` or `180^@`. And `sin0 = sin180 = 0`.

Given two non-zero vectors `vec p, vec q in bbb V` have `vec p xx vec q = 0`, then what is the angle between the vectors?

  • `0^@`
  • `0^@`
  • `90^@`
  • `270^@`
  • Any one of the above

The answer is '`0^@`'. It can either be `0^@` or `180^@`.

 •  Cross product of parallel vectors is 0 or null vector.

Cross Product of Collinear Vectors: For any pair of collinear vectors `vec p, vec q in bbb V`,
`vec p xx vec q =0 `

Angle between vectors when cross product is `0`: For any pair of non-zero vectors `vec p, vec q in bbb V`, If `vec p xx vec q = 0` then the vectors are collinear. The angle between them is `0^@` or `180^@`.

Solved Exercise Problem:

Given `vec p= 2i+3.1j+.5k` and `vec q = 2i+3.1j+.5k` what is the angle between them?

  • `90^@`
  • `45^@`
  • `180^@`
  • `0^@`
  • `0^@`

The answer is '`0^@`'. The vectors are identical.

Solved Exercise Problem:

Given a vector `vec p` with magnitude `12`, what is `vec p xx vec p`?

  • `12`
  • `sqrt(12)`
  • `12xx12`
  • `0`
  • `0`

The answer is '`0`'.

                            
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