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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.
mathsVector AlgebraProperties of Vectors

### Magnitude of a Vector

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

click on the content to continue..

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

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

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

Magnitude of a Vector: For a vector vec p = ai+bj+ck the magnitude is
|vec p| = 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
• obviously it is both the above

Guess what, you are right.

Solved Exercise Problem:

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)
• sqrt(2^2+4^2-2^2)
• 2+4-2
• 2+4+2

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

slide-show version coming soon