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Old 19th March 2012, 10:24 PM   #1 (permalink)
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Some maths qn

stuck at bi)

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Old 19th March 2012, 10:32 PM   #2 (permalink)
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Re: Some maths qn

wow uni maths sio.

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Old 19th March 2012, 10:44 PM   #3 (permalink)
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Re: Some maths qn

Originally Posted by aj5122003 View Post
wow uni maths sio.
It's just A level stuffs. lol.

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Old 19th March 2012, 11:20 PM   #4 (permalink)
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Re: Some maths qn

Which part of the question do you require assistance?

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Old 19th March 2012, 11:21 PM   #5 (permalink)
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Re: Some maths qn

Originally Posted by whitecorp View Post
Which part of the question do you require assistance?
part bi)

[10characters...]

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Old 19th March 2012, 11:28 PM   #6 (permalink)
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Re: Some maths qn

There you go:



Hope this helps. Peace.

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Old 20th March 2012, 12:34 AM   #7 (permalink)
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Re: Some maths qn

Opps... i misinterpreted the question. i joined positional vector 3/-2/7 to plane and says that it's parallel to line 1.

Oh yeah.. here's a DE question, can't show first part. o.o


=====================
another question. Can't do the one in red rectangle.

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Old 20th March 2012, 09:38 AM   #8 (permalink)
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Re: Some maths qn

I have worked these out previously on my site:

http://www.whitegroupmaths.com/2010/...equations.html (see Q8)

http://www.whitegroupmaths.com/2010/...hematical.html ( see Q4)

Hope this helps. Peace.

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Old 20th March 2012, 07:29 PM   #9 (permalink)
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Re: Some maths qn

Originally Posted by whitecorp View Post
I have worked these out previously on my site:

http://www.whitegroupmaths.com/2010/...equations.html (see Q8)

http://www.whitegroupmaths.com/2010/...hematical.html ( see Q4)

Hope this helps. Peace.
Oh lololol! i got these from some maths site.

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Old 20th March 2012, 10:15 PM   #10 (permalink)
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Re: Some maths qn

I have a vectors question too!

How do I find the shortest distance between two planes? I've seen many formulas but I don't really understand how they work. Whitecorp, your vector's summary said something about putting a minus sign between the two modulus' if k1 and k2 have different signs. And about putting a plus sign if k1 and k2 have the same signs. I'm not sure how that works. o.O

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Old 20th March 2012, 10:36 PM   #11 (permalink)
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Re: Some maths qn

When k1 and k2 are of the same sign ( either both positive or negative), then it means that both planes are on the same side of the origin.Hence, to find the distance between the two planes, it is a subtraction of the separate distances of the two planes to the origin. If one is positive while the other is negative, then the two planes are each on the opposite side of the origin; hence the distance between them is achieved by adding them.

Perhaps this in depth explanation on my site would help:

http://www.whitegroupmaths.com/2010/...matters-4.html

Hope this helps. Peace.


Last edited by whitecorp; 20th March 2012 at 10:36 PM.
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Old 20th March 2012, 10:41 PM   #12 (permalink)
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Re: Some maths qn

Ah thanks! Is it possible to change the sign of k to make things simpler? Like, x - 3y - 2z = -4 change to -x +3y + 2z = 4. I think that'll give a different answer though.

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Old 20th March 2012, 10:57 PM   #13 (permalink)
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Re: Some maths qn

It won't make any difference even if you change signs. An example would make things clearer:

Eg. Find the distance between the planes x - 3y - 2z = -4 and -x +3y + 2z = 3

So x - 3y - 2z = -4 -----------(1) and -x +3y + 2z = 3------------------(2)

Notice that the normals to both planes (while parallel) are running in opposite directions. So
you either modify (1) to give -x+3y+2z= 4 or modify (2) to give x-3y-2z= -3. This creates the realization that both planes are actually on the same side of the origin (and not on the opposite side as misleadingly given by the values -4 and 3 on the RHS of (1) and (2) ), and the distance between them is (4-3)/sqrt(14) =1/sqrt(14) units.

Bear in mind when we find distances between planes, we are finding distances between parallel planes, because the distance between two non parallel planes is simply zero. ( ie they will definitely intersect)

Hope this helps. Peace.


Last edited by whitecorp; 20th March 2012 at 11:01 PM.
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Old 20th March 2012, 11:03 PM   #14 (permalink)
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Re: Some maths qn

Oh! I just realized n has to be in the same direction for both planes! Thanks for clarifying. :)

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Old 20th March 2012, 11:05 PM   #15 (permalink)
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Re: Some maths qn

No problem. Peace.

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Old 24th March 2012, 11:20 PM   #16 (permalink)
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Re: Some maths qn

Originally Posted by whitecorp View Post
When k1 and k2 are of the same sign ( either both positive or negative), then it means that both planes are on the same side of the origin.Hence, to find the distance between the two planes, it is a subtraction of the separate distances of the two planes to the origin. If one is positive while the other is negative, then the two planes are each on the opposite side of the origin; hence the distance between them is achieved by adding them.

Perhaps this in depth explanation on my site would help:

http://www.whitegroupmaths.com/2010/...matters-4.html

Hope this helps. Peace.
What happens if the point A lies directly above the origin?
Can we use the same concept? (Length of projection)

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Old 26th March 2012, 02:25 PM   #17 (permalink)
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Re: Some maths qn

Originally Posted by .Memo View Post
What happens if the point A lies directly above the origin?
Can we use the same concept? (Length of projection)
If A lies directly above O, then the vector OA will be parallel to the normal vector of the plane (which can be seen very easily from the plane equation in either scalar product or cartesian form), in which case the magnitude of the vector OA will be the shortest distance from O to the plane. There is no need to use the concept of projection vectors. Hope this helps. Peace.

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