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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.
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.

click on the content to continue..

When two vectors are called '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
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