## Can Skew Lines Be Perpendicular

In a math textbook for primary school, there’s a picture like the one below. They explain which of the line segments are perpendicular and which are parallel to AD.

There’s also a note stating that A1B1, D1C1, BB1 and CC1 are neither parallel nor perpendicular to AD.

I was wondering about that statement, because I learned that those four are perpendicular to AD. So I wrote to the book publisher asking about that. They replied that actually there are two conventions for this situation and they choose “not perpendicular” which, according to them, is more popular.

Is there really no consensus on that?

Edit:I found another question here, related to a mathematical consensus: Is $0$ a natural number? and I’d accept an answer referring to some resources and clarifying whether the consensus exists or not.

## The Distance Between Skew Lines

Look at the figure below. You can see two lines from the three-dimensional Cartesian plane. As is evident from the figure, the shortest distance between the lines is one which is perpendicular to both the lines as compared to any other lines that joins these two skew lines.

We will now move on to how the shortest distance i.e. the length of the perpendicular to two skew lines can be calculated in Vector form and in Cartesian form.

## Applications Of Skewed Data

Skewed data arises quite naturally in various situations. Incomes are skewed to the right because even just a few individuals who earn millions of dollars can greatly affect the mean, and there are no negative incomes. Similarly, data involving the lifetime of a product, such as a brand of light bulb, are skewed to the right. Here the smallest that a lifetime can be is zero, and long lasting light bulbs will impart a positive skewness to the data.

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## Examples Of Skew In A Sentence

*skewing**skewing**skew **WSJ**skew **Quartz**skew **Time**skew **al**skew **Forbes**skew **San Francisco Chronicle**skew **Variety**skew **Washington Post**skew **San Francisco Chronicle**skew **The Atlantic**skew **Star Tribune**skew **Forbes**skew **The Atlantic**skew **Rolling Stone**skew **San Francisco Chronicle**skew **The Atlantic**skew **Los Angeles Times**skew **orlandosentinel.com**skew **Variety**skew **The Indianapolis Star**skew**Forbes**skew **Forbes**skew **National Review**skew **Forbes*

These example sentences are selected automatically from various online news sources to reflect current usage of the word skew. Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

## Definition Of Line Segment

In mathematics, line segment and line are essential concepts for constructing geometrical shapes. In geometry, a line segment is the part of the line with a fixed distance. We can say that the line segment has a finite length, whereas the line does not have any fixed size.

As per Euclids concept, a line is a breadthless length. A line is an essential geometric figure, which connects all points on it. A line has no endpoints, and it extends infinitely in both directions. A line segment is a part of the line. A line segment connects any of the two points on the line. The part or portion of the line between points \ and \ is called the line segment in the figure below. Thus, \ is the line segment.

The line segment is connected way of the two points, which you can measure. Line segments are utilised to form the sides of the polygon.

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## Solved Example For You

**Question 1: Find the shortest distance between the lines whose equations are:**

**$$ \vec_1 = \vec + \vec + \lambda $$**

**$$ \vec_2 = 2 \vec + \vec \vec+ \mu $$**

**Answer:** We shall compare the given equations with the standard form i.e. \vec_1 = \vec_1 + \lambda \vec_1 and vec_2 = \vec_2 + \mu \vec_2. Accordingly, we have:

$$ a_1 = \vec + \vec , b_1 = 2 \vec \vec + \vec $$

$$ a_2 = 2 \vec + \vec \vec , b_2 = 3\vec 5 \vec + 2 \vec $$

So, we can find the shortest distance as :

$$ d = | . | / | \times | $$

= | 3 0 + 7 | / 1/2

= |10| / 1/2 is the shortest distance between the given lines.

**Question 2: How does the skew lines look like?**

**Answer:** The skew lines are those lines which do not intersect, but also never lie on a similar plane. They look like they are running in similar directions and even look totally random.

**Question 3: Can skew lines be perpendicular?**

**Answer:** A line is said to be perpendicular to the other line only if they are intersecting at a right angle, and we know that the skew lines never intersect or meet, so, the skew lines can never become a perpendicular.

**Question 4: What are the dissimilarities between the parallel lines and the skew lines?**

**Answer:** The most common difference between the parallel lines and the skew lines is that the parallel lines lie in a similar plane whereas the skew lines lie in dissimilar planes.

**Question 5: How can we prove the skew lines?**

## Line: Definition Diagrams Types And Examples

In geometry, it is common to say a line segment and lines are the same. A **Line** segment has a definite beginning and a definite end, but a line is extended towards infinity at both ends. Examples of line segments include the length of a table, the distance of a straight road, etc. A segment is part of a line, but a line is not part of a segment. Lets learn about lines, their types and some real-life examples.

Horizontal, vertical lines, parallel and perpendicular lines are examples of different types of lines. A line is a one-dimensional figure, which has length but no width. A line is made up of a series of points that are infinitely stretched in opposite directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line. Continue reading this article to know more about Line.

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## What Are Skew Lines

Before learning about skew lines, we need to know three other types of lines. These are given as follows:

- Intersecting Lines – If two or more lines cross each other at a particular point and lie in the same plane then they are known as intersecting lines.
- Parallel Lines – If two are more lines never meet even when extended infinitely and lie in the same plane then they are called parallel lines.
- Coplanar Lines – Coplanar lines lie in the same plane.

## Skew Lines And Ruled Surfaces

If one rotates a line L around another line L’ skew but not perpendicular to it, the swept out by L is a . For instance, the three hyperboloids visible in the illustration can be formed in this way by rotating a line L around the central white vertical line L’. The copies of L within this surface make it a it also contains a second family of lines that are also skew to L’ at the same distance as L from it but with the opposite angle. An of this ruled surface produces a surface which in general has an elliptical cross-section rather than the circular cross-section produced by rotating L around L’ such surfaces are also called hyperboloids of one sheet, and again are ruled by two families of mutually skew lines. A third type of ruled surface is the . Like the hyperboloid of one sheet, the hyperbolic paraboloid has two families of skew lines in each of the two families the lines are parallel to a common plane although not to each other. Any three skew lines in **R**3 lie on exactly one ruled surface of one of these types .

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## Shortest Distance Between Two Skew Lines

The shortest distance between two skew lines is given by the line that is perpendicular to the two lines as opposed to any line joining both the skew lines.

The vector equation is given by d = |\}}\times\overrightarrow}|}\)| is used when the lines are represented by parametric equations

The cartesian equation is d = \ is used when the lines are denoted by the symmetric equations.

## Parallel And Skew Lines

Parallel lines are two lines in the same plane that remain at a constant distance from each other and never intersect.In a coordinate plane, parallel lines can be identified as having equivalent slopes. Parallel lines aretraditionally marked in diagrams using a corresponding number of chevrons .

Skew lines are two lines not in the same plane that do not intersect. Parallel and skew lines are also important concepts in Algebra and upper-level math courses.

**What are intersecting and parallel lines?**Intersecting lines are coplanar.Three points determine a plane.Parallel lines never intersect and are coplanar.

**What are skew lines?**Skew lines are noncoplanar and nonintersecting.

**Learn what parallel, skew and intersecting lines are.**Parallel lines are two line in the same plane that do not intersect.

Students learn the definitions of parallel lines, skew lines.Skew lines are non-coplanar lines that do not intersect.

**Parallel Planes and Lines**In Geometry, a plane is any flat, two-dimensional surface. Two planes that do not intersect are said to beparallel. Parallel planes are found in shapes like cubes, which actually has three sets of parallel planes.The two planes on opposite sides of a cube are parallel to one another.

Two lines in the same plane either intersect or are parallel. If two lines intersect and form a right angle,the lines are perpendicular.

Skew lines are lines that are non-coplanar and do not intersect.

Example:

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## Distance Between Skew Lines

The shortest distance between two skew lines is the length of the line segment that intersects both lines and is perpendicular to both lines. For each pair of skew lines, there is only one line segment that is perpendicular to and intersects both lines.

In the figure above, line segment CD is perpendicular to both lines a and b so its length is the shortest distance between the skew lines a and b above.

## Distance Between Skew Lines Formula

To find the distance between the two skew lines, we have to draw a line that is perpendicular to these two lines. We can represent these lines in the cartesian and vector form to get different forms of the formula for the shortest distance between two chosen skew lines.

Say we have two skew lines P1 and P2. We will study the methods to find the distance between two skew lines in the next section.

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## Test For Perpendicular First Then Intersecting And Then Skew

**Example**

Say whether the lines are parallel, intersecting, perpendicular or skew.

Well start by testing the lines to see if theyre parallel by pulling out the coefficients

???\frac=\frac=\frac???

???\frac53=\frac12=\frac???

Since ???5/3\neq1/2\neq-1/2???, we know the lines are not parallel.

Because theyre not parallel, well test to see whether or not theyre intersecting. Well set the equations for ???x???, ???y???, and ???z??? from each line equal to each other. If we can find a solution set for the parameter values ???s??? and ???t???, and this solution set satisfies all three equations, then weve proven that the lines are intersecting.

Setting ???x_1=x_2???, we get

???x_1=x_2???

Setting ???z_1=z_2???, we get

???z_1=z_2???

???0=7???

Since ???0\neq7???, the lines are not intersecting.

Because ???L_1??? and ???L_2??? are not parallel and not intersecting, by definition they must be skew.

**Two lines are intersecting** if the lines are not parallel or if you can solve them as a system of simultaneous equations.

In the previous example, we didnt test for perpendicularity because only intersecting lines can be perpendicular, and we found that the lines were not intersecting. If we had found that ???L_1??? and ???L_2??? were in fact perpendicular, we would have needed to test for perpendicularity by taking the dot product, like this:

???L_1\cdot L_2=++???

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## Skew Flats In Higher Dimensions

In higher-dimensional space, a flat of dimension *k* is referred to as a *k*-flat. Thus, a line may also be called a 1-flat.

Generalizing the concept of *skew lines* to *d*-dimensional space, an *i*-flat and a *j*-flat may be **skew** if *i* + *j*< *d*. As with lines in 3-space, skew flats are those that are neither parallel nor intersect.

In affine *d*-space, two flats of any dimension may be parallel.However, in projective space, parallelism does not exist two flats must either intersect or be skew.Let *I* be the set of points on an *i*-flat, and let *J* be the set of points on a *j*-flat.In projective *d*-space, if *i* + *j* *d* then the intersection of *I* and *J* must contain a -flat.

In either geometry, if *I* and *J* intersect at a *k*-flat, for *k* 0, then the points of *I* *J* determine a -flat.

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## What Are Skew Lines In Geometry Slidesharedocs

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## Can Lines On Different Planes Be Parallel

In Geometry, a plane is any flat, two-dimensional surface. Two planes that do not intersect are said to be parallel. Parallel planes are found in shapes like cubes, which actually has three sets of parallel planes. But a line and plane can be parallel to each other and two planes can be parallel to each other.

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## Measures Of Shape: Skewness And Kurtosis

**Summary:****measures of shape****skewness tells you the amount and direction of skew****kurtosis tells you how tall and sharp the central peak is**

Why do we care? One application is**testing for normality**: many statistics inferences require thata distribution be normal or nearly normal. A normal distribution hasskewness and excess kurtosis of 0, so if your distribution is close tothose values then it is probably close to normal.

**Technology:**

- MATH200B Program Extra Statistics Utilities for TI-83/84 has a program to download toyour TI-83 or TI-84. Among other things, the program computesall the skewness and kurtosis measures in this document.
- Theaccompanying Excel workbookperforms two tests for normality, including theDAgostino-Pearson test described below.

**Contents:**

## What Is A Skew Angle

The term angle of skew or skew angle is basically the angle between a normal/perpendicular to the alignment/centerline of the bridge and the centerline of the pier . Thus, on a straight bridge, the skew angle at all supports would normally be the same and the term skew angle can be applied to the bridge as a whole

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## Different Types Of Lines In Geometry Basic Definition And Examples

A line is a one-dimensional geometric figure having length but no width. It is made up of points that are extended in opposite directions infinitely. The different types of lines are horizontal, vertical, parallel, perpendicular, curved, and slanting lines. The definitions of each type of line with an image are given below. Go through the entire article to learn in detail about the Types of Lines in Geometry and examples for each one of them.

## What Is The Definition Of Skew In Math

**geometry****skew****skew**

. Likewise, what is skew lines with examples?

**Skew lines** are straight **lines** in a three dimensional form which are not parallel and do not cross. An **example** of **skew lines** are the sidewalk in front of a house and a **line** running across the top edge of a side of a house.

Secondly, are skew lines perpendicular? **Skew lines** are **lines** that are in different planes and never intersect. A line is said to be **perpendicular** to another line if the two **lines** intersect at a right angle. Learn **skew** line, parallel and **perpendicular lines** along with **skew** line exmaples with the help of resources on this page.

Consequently, which definition best describes skew lines?

**Skew lines** are two **lines** that do not intersect and are not parallel. Two **lines** that both lie in the same plane must either cross each other or be parallel, so **skew lines** can exist only in three or more dimensions . Two **lines** are **skew** if and only if they are not coplanar .

Are parallel lines coplanar?

Two **lines are parallel lines** if they are **coplanar** and do not intersect. **Lines** that are not **coplanar** and do not intersect are called skew **lines**. Two planes that do not intersect are called **parallel** planes.

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## Asset Prices As Examples Of A Skewed Distribution

The departure from normal returns has been observed with more frequency in the last two decades, beginning with the internet bubble of the late 1990s. In fact, asset returns tend to be increasingly right-skewed. This volatility occurred with notable events, such as the Sept. 11 terrorist attacks, the housing bubble collapse and subsequent financial crisis, and during the years of quantitative easing .

The unwinding of the Federal Reserve Boards unprecedented easy monetary policy may be the next chapter of volatile market action and more asymmetrical distribution of investment returns. Most recently we saw extreme downside moves during the beginning of the global COVID-19 pandemic.