PLS EXPLAIN......

a . b = a. c

Hence, a.(b-c)=0 ...(1)

Now:

a X b = a X c

Hence:

a X (b- c)=0...(2)

From (1) and (2) both vectors a and b-c are perpendicular as well as parallel. It implies either of them is a zero vector. As a is a non zero vector, b-c=0 Hence b=c.