已知向量a=(1,1),b=(1,0),c满足a·c等于0,且|a|=|c|,b·c＞0.

题目

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!

答案

(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 = 1 or -1( rejected , x>0)y = -1c ( 1,-1)(2)f...