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!!

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- Jul 29th 2008, 02:40 PMTheJacksonaterdot 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, 03:39 PMJhevon
these require some algebraic manipulation.

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

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, 06:19 PMTheJacksonater