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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.
mathsVector AlgebraProperties of Vector Multiplication by Scalar

### Unit Vector along a vector

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 ofvec 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