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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**.

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

think,

figure-out, &

learn.

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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.

nub,

trek,

jogger,

exercise.

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

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Magnitude of a Vector

» magnitude of `vec(p) = ai+bj+ck` is `|vec(p)|= sqrt(a^2+b^2+c^2)`

→ length of `bar(OP)` is the magnitude

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

**Magnitude** of a vector is the 'amount' of the quantity without the direction information.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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In this page, computing magnitude of a vector is explained in detail.

Starting on learning "magnitude of a vector". ;; In this page, computing magnitude of a vector is explained in detail.

What is the length of the `vec(OP)` in the figure?

- `3+4`
- `7`
- both the above
- `sqrt(3^2+4^2)`

Answer is '`sqrt(3^2+4^2)`', which is computed using the formula to find hypotenuse of right angled triangles (Pythagoras theorem).

What is the length of the `vec(OP)` in the figure?

- This does not form any right angled triangles to calculate OP
- `sqrt(3.3^2+2.5^2)`
- `sqrt(3.3^2+2.5^2-3.1^2)`
- `sqrt(3.3^2+2.5^2+(-3.1)^2)`

Answer is '`sqrt(3.3^2+2.5^2+(-3.1)^2)'`.

How this is calculated?

How is the length of the vector `vec OP` calculated?

- length of `bar(ON)` is calculated using `bar(OM)` and `bar(MN)` as sides of a right angled triangle `OMN`
- length of `bar(OP)` is calculated using `bar(ON)` and `bar(NP)` as sides of a right angled triangle `ONP`
- both the above as two steps

Answer is 'both the above'.

This uses Pythagoras Theorem in two steps.

A vector is defined as a quantity with magnitude and direction. If the direction information in removed, the magnitude of a vector is obtained. In this example, length of `bar(OP)` is the magnitude of the vector.

The magnitude of a vector `ai+bj+ck` is given by `sqrt(a^2+b^2+c^2)`

Does the word 'magnitude' has any meaning?

- yes, it means size of something.
- of course, yes, it means size
- obviously it is both the above

Guess what, you are right.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Magnitude of a Vector: ** For a vector `vec p = ai+bj+ck` the magnitude is

`|vec p| = sqrt(a^2+b^2+c^2)`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

A point P is given by the vector `2i+4j-2k`. What is the distance of the point from the origin?

- `sqrt(2^2+4^2+(-2)^2)`
- `sqrt(2^2+4^2-2^2)`
- `2+4-2`
- `2+4+2`

Answer is '`sqrt(2^2+4^2+(-2)^2)`'

*your progress details*

Progress

*About you*

Progress

What is the length of the vector O P in the figure?

3;4

3+4

7

7

both;above

both the above

square;squared;3;4

square root of 3 squared + 4 squared

The answer is "square root of 3 squared + 4 squared". which is computed using the formula to find hypotenuse of right angled triangles (Pythagoras theorem).

What is the length of the vector O P in the figure?

1

2

3

4

The answer is "square root 3 point 3 squared plus 2 point 5 squared plus minus 3.1 squared."

How is the length of the vector O P calculated?

1

2

3

The answer is "both the above". This uses Pythagoras Theorem in two steps.

A vector is defined as a quantity with magnitude and direction. If the direction information in removed, the magnitude of a vector is obtained. In this example, length of O P is the magnitude of the vector. ;; The magnitude of a vector a i+b j+c k is given by square root of a squared plus b squared plus c squared.

Magnitude of a vector is the amount of the quantity without the direction information.

Magnitude of a vector: For a vector p = a i + b j + c k, the magnitude is ;; magnitude of vector p = square root of a squared plus b squared plus c squared.

Does the word magnitude has any meaning?

1

2

3

Guess what, you are right.

A point P is given by the vectors 2 i + 4 j minus 2 k. What is the distance of the point from the origin?

1

2

3

4

The answer is "square root of 2 squared + 4 squared + minus 2 squared.".