已知向量a=(1,1),b=(1,0),c满足a·c等于0,且|a|=|c|,b·c>0.
问题描述:
已知向量a=(1,1),b=(1,0),c满足a·c等于0,且|a|=|c|,b·c>0.
(1)求向量c
(2)若映射f:(x,y)→(x`,y`)=xa+yb,求映射 f下点(1,2)的原象.
以上 a b c 都为向量!
答
(1)|a| = √2let c=(x,y)=> x^2 +y^2 =2 (1)a.c =0(1,1)(x,y) =0=> x+y = 0(2)b.c >0(1,0)(x,y)>0=> x > 0sub (2) into (1)2x^2 = 2x = 1or-1( rejected , x>0)y = -1c ( 1,-1)(2)f...