Question

已知向量a=(2x-y+1,x+y-2),向量b=(2,-2).设向量n和向量m是两个单位向量,其夹角是60°,试求向量

Answer 1

a=(2x-y+1,x+y-2),b=(2,-2)

a.b

=(2m+n).(-3m+2n)

= -6|m|^2 +m.n + 2|n|^2

= -4+cos60°

= -7/2

also

a.b = |a||b|cosα ( α :a,b夹角)

-7/2= 2√ 2(√((2x-y+1)^2 + (x+y-2)^2)) cosα

cosα = -7√ 2/[8(√((2x-y+1)^2 + (x+y-2)^2))]