# dot product property proof help

• Jul 29th 2008, 03:40 PM
TheJacksonater
dot product property proof help
Hey guys, I need help proving the following two dot product properties using 3 space vectors.
1) s (a . b ) = sa . b = a . sb, s being a scalar, a and b being vectors

2) That it is distributive, i.e. a . (b . c) = a . b + a . c

Thanks!!
• Jul 29th 2008, 04:39 PM
Jhevon
Quote:

Originally Posted by TheJacksonater
Hey guys, I need help proving the following two dot product properties using 3 space vectors.
1) s (a . b ) = sa . b = a . sb, s being a scalar, a and b being vectors

2) That it is distributive, i.e. a . (b . c) = a . b + a . c

Thanks!!

these require some algebraic manipulation.

let $\bold{a} = \left< a_1, a_2, a_3 \right>$, $\bold{b }= \left< b_1, b_2, b_3 \right>$, and $\bold{c} = \left< c_1, c_2, c_3 \right>$

now just plug them in on the right side of each equation and simplify so that you get the left side. or, alternatively, expand both sides and show that you get the same thing
• Jul 30th 2008, 07:19 PM
TheJacksonater
Quote:

Originally Posted by Jhevon
these require some algebraic manipulation.

let $\bold{a} = \left< a_1, a_2, a_3 \right>$, $\bold{b }= \left< b_1, b_2, b_3 \right>$, and $\bold{c} = \left< c_1, c_2, c_3 \right>$

now just plug them in on the right side of each equation and simplify so that you get the left side. or, alternatively, expand both sides and show that you get the same thing

Yup, I follow along that I'm suppose to use a1, a2, etc.... but I am having trouble with the algebraic manipulation.

Edit: nvm, solved it.