数学向量题

显示全部楼层 · 2009-2-26 15:41:06

已知向量A等于向量Y减向量X，向量B等于2倍的向量X减向量Y,向量A的模等于向量B的模等于1，向量A乘向量B等于0，求向量X的模加向量Y的模等于多少

千问 · 2009-2-26 15:41:06

A = Y - X,B = 2X - Y,A + B = X,Y = X + A = 2A + B,A*B = B*A = 0.A*A = |A|^2 = 1,B*B = |B|^2 = 1.|X|^2 = X*X = (A+B)*(A+B) = A*A + B*A + A*B + B*B = 1 + 0 + 0 + 1 = 2,|X| = 2^(1/2)|Y|^2 = Y*Y = (2A + B)*(2A + B) = 4A*A + 2B*A + 2A*B + B*B = 4 + 0 + 0 + 1 = 5,|Y| = 5^(1/2)|X| + |Y| = 2^(1/2) +...

千问 · 2009-2-26 15:41:06

a=y-xb=2x-y,所以,通过解x，y得：x=a+by=2a+bx^2=(a+b)^2=a^2+b^2+2*ab=2y^2=(2a+b)^2=4a^2+4ab+b^2=5所以：|x|+|y|=√2+√5...

千问 · 2009-2-26 15:41:06

不妨作等腰直角三角形ABC(B=90)延长CA至D使AD=AC,连结DB，则AB为a,BC为b,DA为X,DB为Y。又AB=CB=1，则AC=AD=√2,DB=√5（余弦定理）,故x+y=√2+√5...

千问 · 2009-2-26 15:41:06

根号2+根号5 由于符号不好表示，过程复杂只好给你结果...

千问 · 2009-2-26 15:41:06

a\ = y\ - x\ b\ = 2x\ - y\ |a\| = |b\| = 1 a\.b\ = 0 => x\ = a\ + b\ y\ = 2a\ + b\ |x\|^2 = 2|y\|^2 = 5|x\| + |y\| =√2+√5...