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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

In this page, learn how to compute unit vector along a vector.

click on the content to continue..

Given the magnitude of a vector `|vec p| = 20` what is the magnitude of `(vec p)/5`?

  • `20`
  • `5`
  • `4`
  • `4`
  • `1/4`

The answer is '4'. It is `(|vec p|)/(|5|)`.

Given the magnitude of a vector `|vec p|` what is the magnitude of `(vec p)/(|vec p|)`?

  • 1
  • 1
  • `|vec p|`
  • `-1`
  • `-|vec p|`

The answer is '1'.

Given two vectors `vec p` and `vec q`, how can you verify if the vectors are in same direction?

  • directional cosines should be equal
  • directional cosines should be equal
  • components along axes should be equal

The answer is 'Directional Cosines should be equal' along the respective axes.

Given two vectors `vec p` and `(vec p)/2`, are these in the same direction?

  • Different directions
  • Opposite directions
  • Same direction
  • Same direction

The answer is 'Same Direction'. Direction cosine of `(vec p)/2` is same as that of`vec p`. Please verify this by working out.

It is shown that
 •  magnitude of `(vec p)/(|vec p|)` is `1`
 •  direction of `(vec p)/(|vec p|)` is same as that of `vec p`

 •  Unit vector in the direction of a vector is the vector divided by its magnitude.

Unit Vector along a Vector: The unit vector along a given vector `vec p` is given by
`hat p = (vec p)/(|p|)`

Solved Exercise Problem:

Find the unit vector along the direction of vector `vec p = 2i+2j+2k`

  • `1/sqrt(3) (i+j+k)`
  • `1/sqrt(3) (i+j+k)`
  • `i+j+k`
  • `2/sqrt(3) (i+j+k)`

The answer is '`1/sqrt(3) (i+j+k)`'.

slide-show version coming soon