a.b=|a||b|cos@ = a.c=|a||c|cos#
so |b|cos@= |c|cos # |b|/|c|=cos#/cos@
axb=|a||b|sin@ = axc=|a||c|sin#
so |b|sin@ = |c|sin# |b|/|c|=sin#/sin@
Hence,cos#/cos@ = sin#/sin@
sin@/cos@ = sin#/cos#
tan @ = tan #
The cross product and dot product only work when the angle is btw 0 and 180 degree,and tan（x) only have one value in that range.As a result,@=#.
So tan @ = tan #,sin @ = sin #,cos @ = cos #
then b=c