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note that the big dots represents the dot product

1. suppose that [tex]a \bullet b = c \bullet b [/tex] for all vectors [tex]\overrightarrow{b} [/tex]. show that [tex]\overrightarrow{a} = \overrightarrow{c} [/tex].

i suppose i can't simply divide out the b, right? anyway, i tried writing out the components of each vector - for example a=(a1, a2, a3), b=(b1, b2, b3), c=(c1, c2, c3). i got as far as:

(b1, b2, b3) [tex]\bullet[/tex](a1-c1, a2-c2, a3-c3) = 0

but i don't know how to simplify this further to eliminate the b. any help is appreciated.