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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

In this page, you will learn about the result of vector dot product of orthogonal vectors.

click on the content to continue..

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.

slide-show version coming soon