Growing of a tree is a scalar quantity or a vector quantity?
Answers
Answer: growing tree is a scalar quantity
Explanation:
Scalar Quantities: The physical quantities which are specified with the magnitude or size alone are scalar quantities. For example, length, speed, work, mass, density, etc.
Firstly, let us look at the definition that you have given for a vector, "A quantity which has both direction and magnitude".
If this was true, let us consider Current. It certainly has both magnitude and direction. Does it make it a vector? No. A vector needs to follow triangle/parallelogram laws of vector addition.
The vector addition law is as given below:
From the above diagram, it becomes obvious why current isn't considered a vector.
Next, about time to talk about time.
When we draw a space graph and mark a point on it as (x,y), the co-ordinates x and y are scalar here as they just indicate numbers. Similarly, in space time when we write the co-ordinates as (t,x,y,z) time is just a coordinate and thus can be called a scalar.
Sometime in relativistic mechanics, the word "scalar" is used as a shorthand for Lorentz scalar, these are quantities which do not change under Lorentz transformation. Time changes and hence it isn't a scalar in this sense.
Although proper time (time measured between two events in space time as measured by an observer who passes through both events) is a Lorentz scalar.
so it does not follow the parallelogram theorem of vector so it is considered as scalar not vector
