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Can Vectors Be Added?

Vector is defined as any quantity that features magnitude together with direction. Vector is used to represent pressure, velocity, momentum, displacement, acceleration, force and many more. Mathematical functions like addition and subtraction can be formed on vectors.

The properties of vectors are:

  • Vector possess both magnitudes as well as direction.
  • Vector does not obey the ordinary laws of Algebra.
  • If either the magnitude or direction in the vector change or both change.
  • Vectors are significantly expressed by the bold-faced letters or letter which have an arrow over them.

Vector Addition

Vector addition is a process in which two or more vector quantities are added. Vector addition is performed depending on the direction of the vector quantities. Vector addition is classified into 2 types:

  • Parallelogram law of vector addition
  • Triangular law of vector addition

Consider a vectors

The method of vector addition is performed on the arrangement of the head and tail of vectors.

  • If 2 vectors are arranged head to tail the triangular law of vector addition is followed.
  • If 2 vectors are arranged head to head or tail to tail then, the parallelogram law of vector addition is followed.

Parallelogram law of vector addition

Parallelogram law of vector addition is performed if 2 vectors are arranged head to head or tail to tail. “If 2 vectors are supposed to be in the adjacent sides of a parallelogram, then the resultant of 2 vectors is provided by the vector that is a diagonal passing through the point of contact of 2 vectors.”

Parallelogram law of Sscchslinfo.in is represented stepwise below

Consider vectors  and  as represented below.

Bring the tail of near . Figure as shown below:

Draw lines from  and  to form a parallelogram without changing the magnitude and direction of the vectors as shown in the figure below.

And this is the resultant vector is given by

+=

Triangular law of vector addition

Triangular law of vector addition is performed when the vectors are in head to tail arrangement

“When two vectors are represented by 2 sides of a triangle in magnitude and direction were taken in the same order then the third side of that triangle represents in magnitude and direction the resultant of the vectors.”

Triangular law of vector addition is represented stepwise below.

Consider vectors  and as represented below.

Bring the head of  to the tail of  the direction and magnitude of the vectors remain unchanged.

Join the tail of to the head of  by a straight line with an arrow pointing towards the head of

The resultant vector is given by

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Casimir effect was discovered in 1948, by Hendrik Brugt Gerhard Casimir the Dutch physicist.

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