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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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.continue

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.continue

Welcome to **nub****trek**.

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The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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.

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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.

*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.

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

*your progress details*

Progress

*About you*

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.