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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

Vector Dot Product

Voice

Voice

Home

Dot Product with Added Direction

»  By definition, dot product is scalar

»  Some applications may specify an additional direction in the multiplication of components in parallel. In such cases, the direction is combined.

Dot product with Added Direction

plain and simple summary

nub

plain and simple summary

nub

dummy

Vector dot product by definition is a scalar. Depending on the application requirement, a direction can be added to the scalar.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, learn about adding direction to the scalar product with an example.

Keep tapping on the content to continue learning.
Starting on learning "Dot product with added direction". ;; In this page, learn about adding direction to the scalar product with an example.

An object by position vector vec p casts a shadow on a screen. The screen in given by unit vector vec s Is the shadow a vector or scalar?

• a vector
• a scalar

The answer is 'a vector'. The shadow is a vector that spans as a ray with a starting and end point.

vec p and the screen hat s are given. what is the length of the shadow?

• vec p cdot hat s
• length is a scalar |p| cos theta
• both the above

The answer is 'Both the above'.

An object by position vector vec p casts a shadow on a screen. The screen in given by unit vector vec s. We saw that the shadow is a vector and the length of the shadow is vec p cdot hat s. Is the shadow as a vector?

• (vec p cdot hat s) hat s
• (vec p cdot hat s) hat p
• (vec p cdot hat s) vec p

The answer is '(vec p cdot hat s) hat s'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Projection vector using Dot Product: For a vector vec p and a direction given by unit vector hat s, the projection vector of vec p in direction hat s is (vec p cdot hat s) hat s.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Progress

Progress

An object by position vector p casts a shadow on a screen. The screen in given by unit vector s. Is the shadow a vector or scalar?
vector
a vector
scalar
a scalar
The answer is 'a vector'. The shadow is a vector that spans as a ray with a starting and end point.
vector p and screen unit vector s are given. what is the length of the shadow?
1
2
3
The answer is 'Both the above'.
An object by position vector p casts a shadow on a screen. The screen in given by unit vector s. We saw that the shadow is a vector and the length of the shadow is vector p dot hat s. Is the shadow as a vector?
1
2
3
The answer is "vector p dot hat s".
Vector dot product by definition is a scalar. Depending on the application requirement, a direction can be added to the scalar.
Projection vector using Dot Product: For a vector p and a direction given by unit vector s, the projection vector of vector p in the direction s is ; vector p dot vector s multiplied by vector s.

we are not perfect yet...