# Why does (a.b).c make no sense?

by uzman1243
Tags: sense
 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?
Mentor
P: 21,397
 Quote by uzman1243 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?
Because the dot product is defined ONLY for two vectors. You can multiply a vector by a scalar, and this is called scalar multiplication.
P: 37
 Quote by Mark44 Because the dot product is defined ONLY for two vectors. You can multiply a vector by a scalar, and this is called scalar multiplication.
But why? is there any proofs as to why this is defined this way?

P: 1,100
Why does (a.b).c make no sense?

 Quote by uzman1243 But why? is there any proofs as to why this is defined this way?
Have you tried it? Write down the definition of a dot product. Make up and write down three vectors and perform the calculation.

(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.)
 Sci Advisor P: 2,951 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".
P: 37
 Quote by Matterwave 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".
thank you!
 Sci Advisor P: 2,951 No problem. =]
Mentor
P: 21,397
 Quote by uzman1243 But why? is there any proofs as to why this is defined this way?
A definition doesn't have to be proved.
P: 366
 Quote by ModusPwnd Can you prove that a cat is not a soda can?
What an unexpected place to find such a gem.

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