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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 Dot Product

Dot product of Collinear Vectors

In this page, you will learn about the result of vector dot 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 dot product as
`vec p cdot vec q = |vec p||vec q|cos theta`
Dot product of collinear vectors What is `vec p cdot vec q`, when the given vectors are collinear?

  • `|p||q|cos 0`
  • `|p||q|cos 180`
  • one the above
  • one the above

The answer is 'one the above'. The angle between Collinear vectors can be either `0^@` or `180^@`.

 •  Dot product of parallel vectors is product of the magnitudes of the vectors.
Dot product of anti-parallel vectors is negative of product of the magnitudes of the vectors.

Dot Product of Collinear Vectors: For any pair of collinear vectors `vec p, vec q in bbb V`,
If they are parallel making `0^@` angle
`vec p cdot vec q =|p||q| `

If they are anti-parallel making `180^@` angle,
`vec p cdot vec q =-|p||q| `

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 cdot vec p`?

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

The answer is '`12xx12`'.

                            
slide-show version coming soon