Question

已知向量m n的夹角为45°则|m|=1,|n|=根号2又向量a=2m+n b=-3m+n

Answer 1

(1) |a|^2=a*a=(2m+n)(2m+n)=4mm+4mn+nn=4+4根号2根号2|2+2=10

|b|^2=bb=(-3m+n)^2=9mm-6mn+nn=9-6+2=5

ab=(2m+n)(-3m+n)=-6mm-mn+nn=-6-1+2=-5

cos(a,b)=-5/根号50=-根号2/2

a,b夹角是135度

(2) c=ta-b d=2m-n

cXd=(ta-b)X(2m-n)=(2tm+tn+3m-n)X(2m-n)=((2t+3)m+(t-1)n)X(2m-n)

=-(2t+3)mXn+2(t-1)nXm

=(2t+3+2t-2)nXm=0向量

4t+1=0 t=-1/4