
#1
Jul3008, 11:18 PM

P: 23

I've been reading and studying from 'Engineering Mechanics  STATICS 5th edition' by Beford and Fowler and it says that the definition of the unit vector e is that it has a magnitude of 1.
Then e.g. V = Ve Then isn't it just V = V? I still find unit vectors pointless/confusing. I need some enlightment on this. 



#2
Jul3108, 02:10 AM

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PF Gold
P: 562

A boldface letter represents a vector. Therefore V is a vector.
A plainface letter (unbolded) is a scalar quantity (which has no direction). So, V is a scalar. Now, if you write V = V then you're saying "the scalar V is equal to the magnitude of the vector V". But you cannot write V = V, obviously, since one object is a vector and the other is a scalar. So, what does this mean: V = Ve ? What this says is "vector V equals the modulus of vector V (i.e. a scalar having the magnitude of vector V) multiplied by the unit vector e". Recall that a vector multiplied by a scalar gives a vector. Writing vector V this way separates out the magnitude of the vector from its direction. The magnitude is V = V, and the direction is the direction of e. Does that help? 



#3
Jul3108, 08:08 PM

P: 23

Also to put it short, do we use unit vectors to specify a certain finite length or interval within a vector of total length V? 



#4
Aug108, 12:21 AM

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P: 562

Unit Vectors (Mechanics)For example, a vector in two dimensions might be written as [tex]\mathbf{v} = 3 \hat{i} + 4 \hat{j}[/tex] where [itex]\hat{i}[/itex] and [itex]\hat{j}[/itex] are unit vectors in the x and y directions. Vector v in this case is a vector of length (magnitude) 5 units, and can be constructed by adding a vector of length 3 pointing in the same direction as the positive x axis and a vector of length 4 pointing in the same direction as the positive y axis. 


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