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Hunus
Can someone help me understand this?
I'm reading a book on classical mechanics and I can't quite catch on to what the author is saying. The scalar product \[\vec r \cdot (d\vec r)= r(d\vec r)_r\]where \[ (d\vec r)_r\] is the projection of \[d\vec r\] on the vector \[\vec r\] This projection is equal to \[d\vec r\] the increment of the magnitude of the vector \[\vec r\] Therefore \[\vec r \cdot (d\vec r)= r*dr\]
|dw:1335174774073:dw|from the sketch you can see\[\vec r \cdot d\vec r= \left| \vec r \right| \left| d\vec r \right| \cos \theta\]and\[ \left| d\vec r \right| \cos \theta=dr\]hence:\[\vec r \cdot d\vec r= r\:dr\]
l dont understand the language of the author but this is a vector as you see that it have direction and magnitube. this vector have components Y&X becouse of the angle on the x-axes so l think this language is explaining that