Scalar Quantities Vs Vector Quantities

Physics involves measuring and predicting various quantities (or physical values) like force. mass. and velocity.These values can be classified into those having only magnitude and those having both magnitude and direction. A quantity that has magnitude without a direc­ tion is referred to as a sea/or quantity. Mass is a scalar quantity. Energy and work are also scalar quantities.

On the other hand. force is a value with a direction. You can see that from the fact that the motion of an object changes if you apply force from a different direction.

A quantity that has a direction is called a vector. Velocity and acceleration and momentum are also vector quantities, as they have direction. You may forget the terms scalar and vector, but you should keep in mind that there are two types of values in physics:

1. Those with just a magnitude 
2. Those with both a magnitude and a direction

Vector: Basics

A vector is represented using an arrow.The length of the arrow represents the magnitude of the vector. and the point represents its orientation. or direction.Two vectors with the same magnitude and direction are equivalent to one another. even if they do not have the same origin.

 

Also note that the magnitude of a vector (represented by the length of the arrow) can be noted with absolute value symbols, like |a| or simply as a.

The sum of two vectors (a + b) is shown by joining the head of vector a to the tail of vector b. and then extending a line from the tail of a to the head of b, as shown in the figure. As this vector is a diagonal of the parallelogram in the figure, it is obvious that it is also equivalent to b + a. Therefore, we know that the following is true:  

Commmunitative Law: a + b = b + a

 

Negative Vector

Vector -a or a preceded by a minus sign, yields a sum of zero when added to Vector a. In an equation, the relationship looks like this: a + (-a) = 0

In terms of geometry, Vector -a is simply vector of the same magnitude as Vector a, but in the exact opposite direction. The 0 on the right side of this equation represents zero as a vector, referred to as a zero vector. When vectors cancel each other out in this way. an object is said to be in equilibrium.

 

Difference between Two Vectors

The difference between two vectors (a - b) can be defined as follows:

Commmunitative Law: a - b = a + (-b)

Thus, we can find the result of the equation using the same process for summing vectors:

 

Multiplying Vectors By Scalars

Doubling vector -a means doubling its magnitude without changing its direction. The result is represented as 2a.

Generally, k multiplied by a (k.a) represents vector with magnitude k times greater than a but in the same direction.

nb: this is a nostalgic note of mine from a book Manga Guide to Physics