→a=(cos25°,sin25°),→b=(sin20°,cos20°),若t是实数,且→c=→a+t→b则∣→c∣的最小值为?

c=a+tb
则,c=(cos25°+tsin20°,sin25°+tcos20°)
则：
|c∣^2=(cos25°+tsin20°）^2+(sin25°+tcos20°)^2
(cos25°)^2+2tcos25°sin20°+(tsin20°）^2+(sin25°)^2+2tcos20°sin25°+(tcos20°)^2
=1+t^2+2tsin(20°+25°)
=1+t^2+√2t
=(t+√2/2)^2+1/2
当t=-√2/2,取得最小值1/2