Question

What are the physical quantities on which vectors and scalers are differentiated?

Answer 1

A scalar quantity is a one dimensional measurement of a quantity, like temperature, or weight. A vector has more than one number associated with it. A simple example is velocity. It has a magnitude, called speed, as well as a direction, like North or Southwest or 10 degrees west of North. You can have more that two numbers associated with a vector. For example you can add a height dimension to velocity and say, for example, ' I am going uphill at a 5 degree slope in the Northeast direction'. Vectors are frequently broken down into their components along an orthogonal coordinate system, like the x and y axes. So you can say the y-component of my speed is 3 km/sec and the x-component of my speed is 4 km/sec. The magnitude, or speed is the square root of the sum of the individual components, 5 in this case. The direction with respect to the x-axis would be given by the arctangent of V_y / Vx or 36.9 degrees

Defining Scalar and Vector Quantity
Scalar is the measurement of a medium strictly in magnitude.
Vector is a measurement that refers to both the magnitude of the medium as well as the direction of the movement the medium has taken.

Scalar Quantities
Scalar quantities, as stated above, are the measurements that strictly refer to the magnitude of the medium. There are absolutely no directional components in a scalar quantity - only the magnitude of the medium.

Time - Scalar quantities often refer to time; the measurement of years, months, weeks, days, hours, minutes, seconds, and even milliseconds.

Volume - Scalar quantity can refer to the volume of the medium, as in how much of the medium is present. Everything from tons to ounces to grams, milliliters and micrograms are all scalar quantities, as long as they are applied to the medium being measured and not the movement of the medium.

Speed and temperature - Two more commonly used scalar quantities in physical calculations are speed and temperature. As long as they are not associated with a directional movement, they remain scalar quantities. For instance, the measurement of speed in miles or kilometers-per-hour or the measurement of the temperature of the medium both remain scalar quantities as long as they aren’t associated with the direction of the medium’s travel.

Vector Quantities
Vector quantities, however, refer to both the direction of the medium’s movement as well as the measurement of the scalar quantity.

Increase/Decrease in Temperature - The measurement of the medium’s temperature is a scalar quantity; the measurement of the increase or decrease in the medium’s temperature is a vector quantity.
Velocity - The measurement of the rate at which an object changes position is a vector quantity. For example:
If a person quickly moves one step forward and then one step backward there would certainly be a lot of activity; but, there would be "zero velocity."
In order to measure the vector quantity of the medium, there must be:
A directional measurement applied to the scalar quantity. For example:
Regardless of how fast an object is going, the direction of the movement must be described in the velocity vector such as "rightwards" or "forward."
A beginning reference point for the directional measurement in order to provide the directional element of the vector quantity. Your beginning point could be centered in a north, south, east and west quadrant so that the vector quantity can be applied to the medium’s movement. For example:
To describe a car's velocity you would have to state it as 70 miles per hour, south.
Another directional element that may be applied to the vector quantity is the different between vertical and horizontal movements.