Question

若a=(cos14,cos76),b=(cos74,cos16),u=a+tb,t属于[-1,1]求a乘b求|u|的最大

Answer 1

(1)a·b=cos14°cos74°+ cos76°cos16°

=cos14°cos74°+ sin14°sin74°

=cos(74°-14°)

=cos60°

=1/2

|a|=1,|b|=1

(2)|u|²=a²+t²b²+2ta·b

=t²+t+1

=(t+1/2)²+3/4

当t=1时,|u|²有最大值3,|u|有最大值√3