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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.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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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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