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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.

User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

Just keep tapping (or clicking) on the content to continue in the trail and learn.

User Guide

To make best use of nubtrek, understand what is available.

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

jogger provides the complete mathematical definition of the concepts.

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

Voice

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»  continuous addition of vec x and vec y
→  vec x = vec a + vec b

→  vec y = vec p + vec q

→  the co-initial diagonal of the parallelogram formed by sides vec x and vec y

### Parallelogram Law

plain and simple summary

nub

plain and simple summary

nub

dummy

Two vectors form a parallelogram and the co-initial diagonal is the sum.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Note: Using Geometry, the triangle property of vector addition can be extended to explain parallelogram property of vector addition. In the coming pages, we establish a different point of view for the same.

Two taps simultaneously fill a bucket. One fills at 20 liter per hour and another fills at 10 liter per hour. What type of addition is this?

A ball rolls with two velocity components 2m/sec at 11^@angle and 1.3m/sec at 67^@ angle. The effective velocity of the ball is calculated using...

• This does not look to be vector addition

answer is 'Continuous addition of vectors' The two vectors are acting together resulting in a vector sum.

A table is pulled by two persons with forces f_a and f_b with an angle theta between the two forces. The effective force on the table is calculated using ....

• This does not look to be vector addition

answer is 'Continuous addition of vectors' The two vectors are acting together resulting in a vector sum.

Continuous addition of two vectors is shown in the figure.
The magnitude of a vector is equivalently shown as length of the ray in a coordinate plane. Let us see how to calculate vec r.

The vectors vec x and vec y can be split into components
•  vec x = vec a + vec b
•  vec y = vec p + vec q

Note that vec b = -vec q
and vec a and vec p are in the same direction.

The component vectors are equivalently rearranged as shown in the figure. How will vec a and vec p interact?

• Subtract in magnitude
• cannot calculate

Answer is 'add in magnitude', as they are in the same direction

The component vectors are equivalently rearranged as shown in the figure. How will vec b and vec q interact?

• cancel out to 0
• subtract in magnitude
• both the above

Answer is 'both the above', as they are in the opposite direction.

Note that the result forms a diagonal to the parallelogram. This is given as the parallelogram property of vector addition.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Parallelogram Property of vector addition when two vectors are added, arrange such that their initial points coincide. In that configuration, complete a parallelogram with the two vectors as the two adjacent sides. The diagonal that starts from the initial point of the vectors is the sum of the two vectors.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Progress

Progress

Note: Using Geometry, the triangle property of vector addition can be extended to explain parallelogram property of vector addition. In the coming pages, we establish a different point of view for the same.
Two taps simultaneously fill a bucket. One fills at 20 liter per hour and another fills at 10 liter per hour. What type of addition is this?
sequential
continuous
A ball rolls with two velocity components 2 meter per sec in 11 degree angle and 1 point 3 meter per sec at 67 degree angle. The effective velocity of the ball is calculated using...
sequential
continuous
does;not;look
This does not look to be vector addition
The answer is "Continuous addition of vector". The two vectors are acting together resulting in a vector sum.
A table is pulled by two persons with forces f a and f b with an angle theta between the two forces. The effective force on the table is calculated using ...
sequential
continuous
does;not;look
This does not look to be vector addition
The answer is "Continuous addition of vectors". The two vectors are acting together resulting in a vector sum.
Continuous addition of two vectors is shown in the figure. The magnitude of a vector is equivalently shown as length of the ray in a coordinate plane. ;; Let us see how to calculate vector r.
The vector x and vector y can be split into components ;; vector x = vector a + vector b ;; vector y = vector p + vector q ;; Note that vector b = minus vector q ;; and vector a and vector p are in the same direction.
The component vectors are equivalently rearranged as shown in the figure. ;; How will vector a and vector p interact?
subtract
Subtract in magnitude
cannot;not;calculate
cannot calculate
Answer is 'add in magnitude', as they are in the same direction
The component vectors are equivalently rearranged as shown in the figure. How will vec b and vec q interact?
cancel;out
cancel out to 0
subtract;magnitude
subtract in magnitude
both;above
both the above
Answer is 'both the above', as they are in the opposite direction.
Note that the result forms a diagonal to the parallelogram. ;; This is given as the parallelogram property of vector addition.
Two vectors form a parallelogram and the co-initial diagonal is the sum
Parallelogram Property of vector addition: when two vectors are added, arrange such that their initial points coincide. In that configuration, complete a parallelogram with the two vectors as the two adjacent sides. The diagonal that starts from the initial point of the vectors is the sum of the two vectors.

we are not perfect yet...