已知正六边形ABCDEF,若向量EA=向量a 向量AC=向量b ,则向量AD用向量a ,b表示为?
问题描述：
已知正六边形ABCDEF,若向量EA=向量a 向量AC=向量b ,则向量AD用向量a ,b表示为?
答
EA =a,AC=b
AD = AC + CD (1)
AD = AE + ED (2)
(1) +(2)
2AD = AC+CD + AE+ED
= b+ CD -a +ED
= b-a + (CD +ED)
= b-a +( FE+ED) ( CD=FE)
= b-a + FD
= b-a + AC ( FD=AC)
= 2b-a
AD = (2b-a)/2