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How we can identify for vectors and scalar quantities

How we can identify for vectors and scalar quantities 
 

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Grade:12th pass

2 Answers

Arun
25750 Points
4 years ago
A vector quantity has a direction and a magnitude, while a scalar has only a magnitude. You can tell if a quantity is a vector by whether or not it has a direction associated with it. Example: Speed is a scalar quantity, but velocity is a vector that specifies both a direction as well as a magnitude
Vikas TU
14149 Points
4 years ago
Dear student 
I will provide a very simple analogy. Suppose you go the market and ask for 1kg of veggies, the shopkeeper wont ask you the direction of measurement. But suppose I ask you to apply say 5N force on a box (assuming you know how much is 5N force), you will immediately ask me in which direction to apply the force? Do you apply in the sides? Or the front face? Or some weird angle? All these will give different outcomes. So you can safely say in the first case, mass is scalar and second case, force is a vector.
Of course this is a very crude method. A more accurate will be a mathematical approach. You select a frame of reference. You measure the quantity. Then change the frame of reference by rotating or translating or both your original co-ordinate axes. If the quantity remain invariant, you have a scalar, or else you have a vector (a more general term would be a tensor).
Edit: I have been asked a very genuine question, that we also think about direction when we think about quantities like pressure which are scalar.
This is a very genuine query, and I am afraid there is no straightforward answer to this. You can say that the law of intuition (as I like to call it) only works for some cases. This is primarily because of the fact that combination of two vectors should not necessarily produce another vector. They can be scalar as well.
So the fact that even for pressure you think about direction, just goes on to show, that this has perhaps got some vector as more basic components like Force and Area vector. So I guess the law of intuition only works for fundamental scalars (which are not combination of vectors) like mass and time and not for scalars which are some combination of two or more vectors like pressure. I would be happy if someone pointed out some more vectors that do not follow the law of intuition and maybe we can then safely come to a much better understanding.

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