 maths > vector-algebra

Standard Unit Vectors

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Overview

Standard Unit Vectors

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

unit means "one"

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

•  $3$$3$m north

•  $4.2$$4.2$m south

•  $\frac{3}{4}$$\frac{3}{4}$ m north

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

The answer is '$5$$5$m '– as the person moved $5$$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}^{\circ }$${90}^{\circ}$ 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$$3$ orthogonal components in 3D coordinate space and $3$$3$ orthogonal axes are defined for that.

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

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

summary

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

Outline