Operation on vectors

Vector Operations

Addition or subtraction of two or more vectors of same type ,yield a single vector whose effect is same as net effect by the vectors which were added or subtracted.

🕮 Addition of a Vector

If individual vectors are parallel with same direction ,the resultant is obtained by adding the individual vectors

                    

🕮 Subtraction of a Vector

If individual vectors are parallel with opposite direction the resultant is obtained by adding the individual vectors.

🕮 Triangle Law for Vector Addition: 

If two vectors describing the same physical quantity are represented in magnitude and direction by the two sides of a triangle taken in order, then their resultant is represented in magnitude and direction by the third side of the triangle drawn in the opposite sense (from the starting point of first vector to the end point of the second vector).

🕮 Laws of  Vector Addition

 * Commutative Law : Vector Addition Obeys Commutative law

  a + b = b + a

* Associative Law : Vector addition obeys associative Law

🕮 Parallelogram Law of  Vector Addition

If two  vectors of the same type starting from the same point, are represented in magnitude and direction by two adjacent side of a parallelogram , then their resultant is represented in magnitude and direction by the diagonal of the parallelogram starting from the same point.

Mathematical Approach for Resultant of a vector starting from same point: 

Consider  two vector P and Q of same type starting from point O making an angle ɵ with each other.

Let us construct a seg BC and AC to complete a parallelogram OACB. As OA ll BC and OB ll AC ,

OB = AC = Q and OA = BC = P. We need to proof OC is a resultant .

_{│<<<Types of vector>>>│  │<<<Resolution of vector>>>│}            

_{Related topics: Mathematical physics      Types of the vector    Vector operation}   

 _{Triangle laws of vector addition       Parallelogram laws of vector addition} 

  _{Resolution of  a vector         Scalar multiplication   Vector multiplication}