The meaning of Finding the largest values

[dgales4130]

Homework Statement

It sounds like a simple question but I am wonder what the scalar properties --mean-- with a problem like this

http://img560.imageshack.us/img560/274/dotproduct.png

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Why/how is the it -6 when they are parallel ? I like the idea of mastering the basics and I can't wrap my head around this scalar value .

Homework Equations

A /dot B ...

The Attempt at a Solution

I know how to do the work but I don't understand. I know why 3*2=6 but I am not sure what this -6 scalar thing mean. I have tried to relate it to the shadow illustration and the ideas of work but I am not real owning the idea.

 

[mtayab1994]

Ok it is really simple scalars are some of the basic things in geometry/w.e. What a scalar/dot value means is ll u ll * ll v ll * cos(uv) and that means that the dot value will be 0 when θ=90° because cos (90)=0 and greatest when theta is 0 because cos(0)=1 degrees and least when theta is 180 degrees because cos(180)=-1.

 

[dgales4130]

When would the value -6 be relevant in terms of work ? or swimming down a river ? Is it a summation of force ? Temperature is a scalar value , I get that but what does this value represent ?

 

[Office_Shredder]

For example when you lift up an object you do a positive amount of work on it, when you lower an object you do a negative amount of work. The positive amount of work means you have to put energy into the system, the negative work corresponds to you (potentially) gaining energy assuming you capture it efficiently.

Temperature being a scalar value and this being a scalar product are two separate things. The word 'scalar' basically just means 'number', in this particular context it means 'not a vector'. We have two vectors, and the scalar product means 'product that is giving us a number, not a vector' (since there does exist a way to "multiply" vectors to get another vector this terminology is used to distinguish the two). Temperatures and scalar products have nothing to do with each other other than the fact that they are both numbers, but then again so are lots of things