Tim Cinel » logic http://www.timcinel.com Where I exercise freedom of speech Tue, 07 Sep 2010 22:00:53 +0000 en hourly 1 http://wordpress.org/?v=3.0 Parallelograms and Vectors http://www.timcinel.com/2008/parallelograms-and-vectors http://www.timcinel.com/2008/parallelograms-and-vectors#comments Sat, 15 Mar 2008 14:40:53 +0000 Tim Cinel http://www.timcinel.com/2008/parallelograms-and-vectors “Again with the maths…” Thursday on the train home, I was trying to solve a maths exercise – I am given A, B and C. I was asked to solve D so that ABCD formed a parallelogram. Where did I start? Here’s what I originally thought:

  • kBC = AD (The top and bottom edges should be parallel)
  • |AB| = |CD| (The two sides would be the same length)

I couldn’t think of any more rules to help me, so I gave made a note of it, then moved on. It wasn’t long until I’d be at it again, and this time I’d solve it.

Paul (again) mentioned that you could use the midpoint between the opposing vertices (A and C ) and (B and X). And that’s how I solved it :)

Here is the proof…

Vector Geometric Solution

If A, B and C are known, solve D so ABCD forms a parallelogram.
Mathamatical Methods for Engineers and Scientists, p7, 1.2.3 Q3

Blast my inferior logic!

]]> http://www.timcinel.com/2008/parallelograms-and-vectors/feed 0 Vectors – Finding a Midpoint Between Two Points http://www.timcinel.com/2008/vectors-finding-a-midpoint-between-two-points http://www.timcinel.com/2008/vectors-finding-a-midpoint-between-two-points#comments Sat, 15 Mar 2008 12:12:02 +0000 Tim Cinel http://www.timcinel.com/2008/vectors-finding-a-midpoint-between-two-points Being the complete twit I am, over the last three days I’ve spent about … one hour, maybe two … trying to work out the coordinates of the midpoint between two points on a 3 dimensional Cartesian plane, using vector addition. It’s all better now, though.

In an example, I was given A(1,-1,3) and B(-2,7,-2)  and I needed to find the midpoint, P.

I was trying to work it out as if P was the same as 1/2(AB) but it’s quite obviously not because that’s only the vector position from point A to point P (halfway Between A and B). Rather, we were looking for the vector position from the origin to the point P. If it wasn’t for Paul, I might still be trying to calculate it like this!

Therefore,  the absolute vector position of point P (midpoint between a and B) can be deducted like:
P = OA + 1/2 * (AB)

Here are the workings for the CORRECT solution :)

Vector Addition - Find Vector Position of Midpoint

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