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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.continue
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?magnitude of a 2D vector example

  • `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?magnitude of a 3D vector example

  • 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?magnitude of a 3D vector example

  • 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

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.

magnitude of a 3D vector example 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)`'

                            
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