maths > vector-algebra

Standard Unit Vectors

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Standard Unit Vectors

 »  3 orthogonal axes are represented with 3 unit vectors
    →  x-axis i
    →  y-axis j
    →  z-axis k

unit means "one"

A person walks 5m east and then takes the following path

 •  3m north

 •  4.2m south

 •  34 m north

At this end position, how far is the person away from the starting point in the east direction ?

The answer is '5m '– as the person moved 5 meter east and then all his movements were in directions north and south.

Any change in a direction affects the component along that direction only and does not affect the components in the directions at 90 to that direction.

Independence of Quantities along orthogonal directions: For a vector, changes along one axis affect only the component along that axis and do not affect the components along other axes, as the axes are orthogonal.

There are 3 orthogonal components in 3D coordinate space and 3 orthogonal axes are defined for that.

Along the three orthogonal axes, irreducible unit is defined as unit vectors i, j, and k.

3D vector space is of 3 orthogonal axes, with standard unit vectors i, j, k.


Standard Unit Vectors: 3D vector space has three orthogonal axes. Unit vectors along the axes are standard unit vectors and are represented with i, j, and k.


The outline of material to learn vector-algebra is as follows.

Note: Click here for detailed outline of vector-algebra.

•   Introduction to Vectors

    →   Introducing Vectors

    →   Representation of Vectors

•   Basic Properties of Vectors

    →   Magnitude of Vectors

    →   Types of Vectors

    →   Properties of Magnitude

•   Vectors & Coordinate Geometry

    →   Vectors & Coordinate Geometry

    →   Position Vector of a point

    →   Directional Cosine

•   Role of Direction in Vector Arithmetics

    →   Vector Arithmetics

    →   Understanding Direction of Vectors

•   Vector Addition

    →   Vector Additin : First Principles

    →   Vector Addition : Component Form

    →   Triangular Law

    →   Parallelogram Law

•   Multiplication of Vector by Scalar

    →   Scalar Multiplication

    →   Standard Unit Vectors

    →   Vector as Sum of Vectors

    →   Vector Component Form

•   Vector Dot Product

    →   Introduction to Vector Multiplication

    →   Cause-Effect-Relation

    →   Dot Product : First Principles

    →   Dot Product : Projection Form

    →   Dot Product : Component Form

    →   Dot Product With Direction

•   Vector Cross Product

    →   Vector Multiplication : Cross Product

    →   Cross Product : First Principles

    →   Cross Product : Area of Parallelogram

    →   Cross Product : Component Form

    →   Cross Product : Direction Removed