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!!
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 $\displaystyle \bold{a} = \left< a_1, a_2, a_3 \right>$, $\displaystyle \bold{b }= \left< b_1, b_2, b_3 \right>$, 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