Question

已知向量a=(1,1\2),b=(0,-1\2),c=a+kb,d=a-b,c与d夹角为派\4,k=?

Answer 1

c=a+bk=(k,1/2-k/2)

d=a-b=(1,1)

cos=c*d/(|c|*|d|)=(1/2+k/2)/(根号（2）*根号（k^2+(1/4)(k-1)^2））=cos(pi/4)=根号(2)/2

解出k=0或1