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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

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Read in the blogs more about the unique learning experience at nubtrek.

User Guide

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think,
figure-out, &
learn.

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User Guide

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nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about.

User Guide

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step.

User Guide

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This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen.

User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Properties of Dot Product

Voice

Voice

Home

»  vector dot product of orthogonal vectors

→  theta = 90^@

→  cos 90^@ = 0

→  vec p cdot vec q = 0

### Dot product of Orthogonal Vectors

plain and simple summary

nub

plain and simple summary

nub

dummy

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

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Starting on learning "Dot product of Orthogonal Vectors". ;; In this page, you will learn about the result of vector dot product of orthogonal vectors.

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

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

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^@
• 180^@
• Any one of the above

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

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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^@.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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

• 90^@
• 0
• 180^@
• 0^@

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

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
• 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.

Progress

Progress

When are two vectors called 'orthogonal' vectors?
90;degree;angle
have 90 degree angle between them
perpendicular;each;other
perpendicular to each other
vectors;right-angled
the vectors are right-angled
all;above
all the above
The answer is 'All the above'
Given the definition of dot product as vector p dot vector q = magnitude of vector p multiplied magnitude of vector q cos theta, what is vector p dot vector q, when the given vectors are orthogonal?
1
2
3
4
The answer is 'All the above'.
Given two non-zero vectors p and q in vector space v, have vector p dot vector q = 0, then what is the angle between the vectors?
0
0 degree
90
90 degree
80;180;hundred
180 degree
Any;one;above
Any one of the above
The answer is "90 degree". It can either be 90 degree or 270 degree.
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 p and q in vector q ;; vector p dot vector q = 0.
Angle between vectors when dot product is 0: For any pair of non zero vectors p, q in vector space v ;; if vector p dot vector q = 0, then the vectors are orthogonal. The angle between them is plus or minus 90 degree.
Given vec p= 2i+j-k and vec q = i+2j+4k what is the angle between them?
1
2
3
4
The answer is "90 degree". As the dot product between the vectors i 0.
Given two vectors p and q in x-y plane, they make angles 13 degree and minus 77 degree with x-axis. What is vector p dot vector q?
1
2
3
4
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.

we are not perfect yet...