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Properties of Vectors

Properties of Vectors

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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

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?magnitude of a 2D vector example

  • `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?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)`

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

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)`

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)`'

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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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