Difference Between Vector Quantity and Scalar Quantity

All the physical quantities we deal with have certain .Mathematical characterstics for instance they are classified as Scalar ,Vectors tensors and so on and so forth . Sometimes they are classified as mathematical operators, matrices and so on .The most common of all these are Scalars and Vectors

Scalar has only magnitude

Whereas,

Vectors have both magnitude and direction

But these definition are not enough .Suppose you look at Coordinate of a point P in a plane.Whose Value in X coordinate is X and in y coordinate is Y

The mathematical quantities that are used to describe the motion of objects can be divided into two categories. The quantity is either a vector or a scalar. These two categories can be distinguished from one another by their distinct definitions:

• Scalars are quantities that are fully described by a magnitude (or numerical value) alone.
• Vectors are quantities that are fully described by both a magnitude and a direction.

The remainder of this lesson will focus on several examples of vector and scalar quantities (distance, displacement, speed, velocity, and acceleration). As you proceed through the lesson, give careful attention to the vector and scalar nature of each quantity. As we proceed through other units at The Physics Classroom Tutorial and become introduced to new mathematical quantities, the discussion will often begin by identifying the new quantity as being either a vector or a scalar.

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.