MYTUTOR SUBJECT ANSWERS

535 views

How do I show two lines are skew?

Skew lines in 3 dimensions are those which are not parallel and do not intersect.

Let's take two example lines: l1 = (2, 2, -1) + λ(3, 1, -3) and l2 = (1, 0, 1) + µ(6, -4, 9)

First we need to show that they are not parallel. To do this we take the direction vectors (the second part with λ or µ constats) and check that one is not a multiple of the other. You can probably see by inspection that this is the case here. To be sure you can divide the first component of one by the first of the other and then check that this is not the same for both of the other components. 

3/6 = 1/2, 1/-4 = -1/4 and -3/9 = -1/3. Here dividing the components by eachother shows that one direction vector is not a multiple of the other since the values are not all the same. So l1 and l2 are not parallel.

Next we need to show that they don't intersect. To do this we can set up three simultaneous equations. Equating the x component of one line to the other and the same for y and z . For example with l1 and l2:

2 + 3λ = 1 + 6µ, equation 1,
2 + λ = 0 - 4µ, equation 2,
-1 - 3λ = 1 + 9µ, equation 3.

To show these don't intersect we need to show that these three equations aren't consistent (so the lines can't cross). One simple way to do this is to determine the value of λ and µ using two of the three equations, then substitute these values into the third equation you haven't used. If the equation is incorrect then they don't intersect. 

For example here I used equations 1 and which gave µ = -1 and λ = -7/3 (I did this by subtracting 1 from 3). If we substitute these values into equation we get 2*(-7/3) = -4*(-1) which gives -1/3 = 4, which is ofcourse incorrect and so these equations aren't consistent and the lines don't intersect. Therefore in this example l1 and l2 are skew.

David  M. A Level Physics tutor, GCSE Physics tutor, A Level Maths tu...

11 months ago

Answered by David , an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

257 SUBJECT SPECIALISTS

£26 /hr

Victor T.

Degree: Economics (Bachelors) - Cambridge University

Subjects offered: Maths, Economics+ 2 more

Maths
Economics
-Personal Statements-
-Oxbridge Preparation-

“Hi I'm Victor and I am a second-year economist at Cambridge having achieved a First last year. I very much enjoy teaching and my aim to instil my passion and enthusiasm for Maths and Economics in my students. I got 12 A*s at GCSE and 5...”

£20 /hr

Alexandra F.

Degree: Archaeology (Bachelors) - Glasgow University

Subjects offered: Maths, Religious Studies+ 2 more

Maths
Religious Studies
English
Chemistry

“I am currently a student at the University of Glasgow studying Maths and Archaeology. I am extremely passionate about science in general but more specifically, maths. I was lucky enough to have several excellent maths teachers through...”

MyTutor guarantee

£30 /hr

Thomas D.

Degree: Economics (Bachelors) - Bristol University

Subjects offered: Maths, Geography+ 2 more

Maths
Geography
Further Mathematics
Economics

“Why choose me? I am a highly academic student having achieved 4 A* at A level but also have excellent communication and mentoring skills havingtutored fellow students at school and beenHead Boy. I am honest, reliable and precise, if ...”

About the author

David M.

Currently unavailable: until 25/11/2016

Degree: Physics (Masters) - Warwick University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Chemistry
.PAT.

“Background I am a second year physics student studying at the University of Warwick. I am passionate about helping people learn and allowing them to attain thehigh grades which they deserve. My love of science and mathematics will com...”

MyTutor guarantee

You may also like...

Posts by David

How do I show two lines are skew?

If the highest frequency a song is 10 kHz and it is encoded at 16 bits per sample what is the minimum number of bytes needed to encode the 3 minute song?

What is the De Broglie wavelength of an electron given it has a kinetic energy of 1 eV? You are given the mass of an electron is 9.11x10^-31 kg and Planck's constant is 6.63x10^-34

Other A Level Maths questions

Find the shortest distance between the line L: x=1+t, y=1+2t, z=1-t and the point A: (2,3,4)

If y = 5x^3 - 2x^2 + 2, what is dy/dx?

What is the derivative of y=(e^(2x))(sin(3x))

Find the equation of the tangent to the curve y=x^3-4x^2+2 at the point (3,-7)

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok