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Thought-Process to Discover Knowledge

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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.

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User Guide

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User Guide

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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 Vectors

Voice

Voice

Home

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

### Magnitude of a Vector

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.

Keep tapping on the content to continue learning.
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

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)'

Progress

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.".

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