Difference Between Perpendicular and Orthogonal

When it comes to geometry and mathematics, numerous terms often seem to mean the same thing but actually, that is not the case! The same is the case of a perpendicular pair and an orthogonal figure.

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Perpendicular vs Orthogonal

The difference between perpendicular and orthogonal is that perpendicular is a phenomenon and it means that a straight line makes a right angle to another line which can never be parallel. The term talks about the ninety-degree angle and the relationship between the two lines whereas, the term orthogonal is rather a condition and a positioning i.e. it describes the relationship between the two lines with respect to each other and not only the angle between them. Let’s talk further about their definition to get more clarity.

Perpendicular vs Orthogonal

They are perpendicular planes, which are straight lines forming two planes that meet at a certain degree – the right angle. “When two planes or lines meet at a 90° angle, we say they are perpendicular”

The phenomenon of this occurrence and this situation where a right angle is formed while the lines are not being parallel to each other is named as a perpendicular.

The vector field may include non-zero self-orthogonal variables based on the bilinear form. Groups of properly functioning are used to build a basis in which values are distributed.

Comparison Table

Parameters of ComparisonPerpendicularOrthogonal
Meaning (Geometric)Perpendicular paths are two separate lines that meet at a 90-degree angle. Orthogonality, when extended to matrices, this feature is equivalent with perpendicularity, although it also applies to functional aspects more broadly.
Relationship1. If two lines meet, one first line is “perpendicular” to the second and vice versa.
2. At the point of incidence, the straight (180) angle on one end of the very first line is split into two corresponding angles by the second plane making them perpendicular as well as orthogonally positive.
1. The property and functional aspect of an orthogonal pair is similar to a perpendicular.
2. The dot product of two vector components of an orthogonal pair is zero.
Statistical RelationThe two lines are statistically dependent and the angles are non-constant if either is changed.The two components of an orthogonal pair are statistically independent of each other.
TerminologyLogical and geometric terminology.Mathematical and geometrical terminology with regards to vector physics.
EtymologyFrom the old French and Latin word ‘perpendicularis’ meaning vertical to the plane.Late 16th century: from French, based on Greek orthogōnios ‘right-angled’.

What is Perpendicular?

When two lines or planes cross at a right angle forming angle, the two lines are seen as being perpendicular to each other.

As a result, we may refer to two planes and lines as perpendicular (to each other) without mentioning their sequence.

All crossing planes or lines are perpendicular to each other, but not all meeting lines are perpendicular to one another. Perpendicular lines have two primary characteristics:

  1. Lines that are perpendicular to one other usually meet or cross.
  2. Any angle formed by two line segments that are claimed to be perpendicular is always 90 degrees.

Do not confuse perpendiculars with “parallels” as they are two straight lines that are separated from one other and never intersect, regardless of how far in either side they are however, perpendiculars even if stretched till infinity, always intersect or rather “cross” each other.

Two perpendicular lines are represented by the symbol: ⊥.

What is Orthogonal?

Orthogonality, when extended to matrices, this feature is equivalent to perpendicularity, although it also applies to functional aspects more broadly.

An inner product structure may be produced from a concatenation of the components of a set of perpendicular vectors or functions, which means that any component of the space can be generated from the members of such a set.

When the partial derivative is a vector, the dot product (see vector operations); for functions, the definite integral of their multiplication—is 0, two components of an n-dimensional space are always orthogonal.

An inner product structure may be produced from a concatenation of the components of a set of perpendicular vectors or functions, which means that any component of the space can be generated from the members of such a set.

Main Differences Between Perpendicular and Orthogonal

  1. Perpendicular also means vertical position whereas other meanings of orthogonal include; “of two or more conditions in a single problem”.
  2. Perpendicular is more suitable in describing the positioning of an object whereas the “orthogonal” term is used to mathematically prove the same condition.
Difference Between Perpendicular and Orthogonal

References

  1. https://www.britannica.com/science/orthogonality
  2. https://www.cuemath.com/geometry/perpendicular/
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