A Scalar quantity is a quantity which only has a magnitude like mass, temperature, light, etc. On the other hand, vectors in Math are objects that have both magnitude and direction. To represent math vectors we use an arrow having a line of given length and pointing along a given direction. The magnitude of a vector is denoted by its length.
For notation, we write it in a bold character with an arrow over it. For example to denote a vector with a magnitude P we can use –
P, P->, P .
P = ai + bj, this is the Position vector, where (a, b) is the terminal Point and the initial point is the origin.
To show the magnitude of the vector we denote it by |A| or simply by A.
A vector that has a magnitude of one that is of unit length is a unit vector. To denote this unit vector we usually use a carat (^) above it.
Here, |a^|= 1
A vector with a magnitude zero is called as null vector. Scalar is a number multiplied in front of a vector. For example in 3X, “3” is a scalar.
Addition of two vectors:
To add vectors, we simply place the initial point that is tail of the second vector on the terminal that is head of the first vector in sequence.
Let us have an example:
To add A = A1a1 + A2a2
B = B1b1 + B2b2
Then, A + B = (A1 + B1)a1 + (A2 +B2)b2
Vector in a coordinate is sum of the components:
F = Fxi + Fxj
F = √F2x + F2y
Here we get,
Fx = F cos theta and Fy = F sin theta
Tan theta = Fy / Fx
This is all about vectors math.
Vectors are generally used to show the direction of any quantity. Generally, there are two type of quantity, one is Scalar and another is vector. Quantity which has only magnitude but no direction is scalar while vectors have both magnitude and direction. For defining the multiplication of vector there are two ways, first is Cross Product Vectors and second is dot pr...Read More
In mathematics, combination of vectors is termed as cross product. Cross product of two vectors ‘P’ and ‘Q’ is represented as p X Q. Sometimes the notation ‘∧’ is also used to represent the cross product. So, sometimes we can write the cross product of two vectors as: P ∧Q.
The cross product of P X Q is defined as a vector ‘c’ which is perpendicular to both the ve...Read More
Scalar quantity is a quantity which only possesses magnitude like mass, temperature, light, etc. To represent Math vectors we use an arrow having a line of given length and pointing along a given direction. The magnitude of a vector is denoted by its length. For notation, we write it in bold character with an arrow over it. For example, to denote a vector with a magnitude ...Read More