1. Given that $a, b, c$ are non-zero planar vectors. Statement A: $a \cdot b=a \cdot c$; Statement B: $b=c$, then
A. A is a sufficient condition for B but not a necessary condition
B. A is a necessary condition for B but not a sufficient condition
C. A is a necessary and sufficient condition for B
D. A is neither a sufficient condition nor a necessary condition for B
1. B Hint: Since $a \cdot b=|a| \cdot|b| \cos \theta$, it follows that $a \cdot b=a \cdot c \neq \Rightarrow b=c$ but if $b=c$, then $a \cdot b=a \cdot c$ so statement A is a necessary but not sufficient condition for statement B