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Why does (a.b).c make no sense?by uzman1243
Tags: sense 
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#1
Apr1514, 11:24 PM

P: 37

I was studying the dot product, and it says that (a.b).c makes no sense.
so if you do (a.b) can = to β and then is it not possible to do β.c? WHY cant you 'dot' a scalar and a vector? why? 


#2
Apr1514, 11:29 PM

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#3
Apr1514, 11:30 PM

P: 37




#4
Apr1514, 11:31 PM

P: 1,105

Why does (a.b).c make no sense?
(Note that definitions are made up, not proved. Can you prove that a cat is not a soda can? No. Its just not defined that way. Theorems and identities are what get proved, under the right definitions.) 


#5
Apr1614, 12:09 AM

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The dot product, in two dimensions (for simplicity) is defined as:
$$\vec{a}\cdot \vec{b}=a_xb_x+a_yb_y$$ Now, this assumes ##\vec{a}=(a_x,a_y)## and ##\vec{b}=(b_x,b_y)## are vectors. What would it mean to turn ##a## into a number? Certainly you can "define" the "dot product" of a scalar and a vector as: $$a\cdot\vec{b}=a\vec{b}=(ab_x,ab_y)$$ But that's just the same as a scalar product, so it would be supremely confusing to also call it a "dot product". That's why we don't call that the "dot product". 


#6
Apr1614, 12:10 AM

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#8
Apr1614, 01:32 AM

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#9
Apr1614, 05:46 AM

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