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Understanding Vectors - Part 2

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Revision as of 06:27, 9 May 2007; view current revision
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In the [Understanding Vectors|last article] we discussed basically what a Vector was and had a brief look at the difference between a Point and a Vector. This time we are going to look at what a Vector is made of and try to really get an understanding of why they are so useful as opposed to a Point. Again, not much math just trying to make the concept clear. What's in a Vector?

Let's have another look at a point and a vector - p(6,8) and v(6,8). Both are 2 dimensional and have 6 units/steps/buses along the x axis and 8 units/steps/buses along the y axis (where units/steps/buses are the units of measure you may be using). Practically the same as you can see but the way you should look and think about them is very different. As we said in the last article, Vectors have a direction and magnitude (or length) and this direction is probably the most useful part of a Vector. To explain this difference a bit further we are going to introduce a few more terms which will make things a bit clearer. Scalars

Scalars can be thought of as the same as units but I like to think of them differently when it comes to Vectors. A unit (for our purposes) is an amount of measurement such as an inch, millimetre or foot that we use to to get to our point by saying something like - "walk 4 feet in the 'x' direction then 6 feet in the 'y' direction" to get to your point. With Vectors you multiply a 'unit' by a 'scalar' to get these distances where a scalar is a 'real' number and not a unit of measurement. It's the same as saying "walk 4 x 1 foot in the 'x' direction...yada, yada". This will become clearer after I explain 'unit vectors'. What's a Unit Vector?

I'm glad you asked! A unit Vector is a vector whose 'length' equals 1 (1 unit of measurement long) and can be in any direction. You can create a unit vector or a 'normalised' vector from any vector and is done quite often when all you need is a 'direction' and not the length. Have a look at the figure below, it shows a circle with a unit radius and random 'unit' vectors( notice these vectors are all equal to the radius of the circle).

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