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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 Orthogonal Vectors

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When are two vectors called 'orthogonal' vectors? color(coral)(text(orth)) + color(deepskyblue)(text(gonia)) means color(coral)(text(right))+color(deepskyblue)(text(angled)).

• have 90^@ angle between them
• perpendicular to each other
• the vectors are right-angled
• 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 orthogonal?

• |p||q|cos 90
• |p||q| 0
• 0
• all the above
• all the above

The answer is 'All the above'.

Given two non-zero vectors vec p, vec q in bbb V have vec p cdot vec q = 0, then what is the angle between the vectors?

• 0^@
• 90^@
• 90^@
• 180^@
• Any one of the above

The answer is '90^@'. It can either be 90^@ or 270^@.

•  Dot product of orthogonal vectors is 0.
If dot product of two non-zero vectors is 0, then the vectors are orthogonal.

Dot Product of Orthogonal Vectors: For any pair of orthogonal vectors vec p, vec q in bbb V,
vec p cdot vec q = 0

Angle between vectors when dot product is 0: For any pair of non-zero vectors vec p, vec q in bbb V, If vec p cdot vec q = 0 then the vectors are orthogonal. The angle between them is +- 90^@.

Solved Exercise Problem:

Given vec p= 2i+j-k and vec q = i+2j+4k what is the angle between them?

• 90^@
• 90^@
• 0
• 180^@
• 0^@

The answer is '90^@'. As the dot product between the vectors is 0.

Solved Exercise Problem:

Given two vectors vec p and vec q in x-y plane. They make angles 13^@ and -77^@ with x-axis. What is vec p cdot vec q?

• 90
• 0
• 0
• 13xx77
• 13xx(-77)

The answer is '0'. The vectors are orthogonal as the angle between them is 13+77. Note that the vectors are in x-y plane.

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