Question

设向量a=（cos55°,sin55°）,b=（cos25°,sin25°）,若t是实数,则|a-tb|的最小值

Answer 1

a-tb=(cos55-tcos25,sin55-tsin25)

|a-tb|=√(cos55-tcos25)^2+(sin55-tsin25)^2

=√cos55^2-2tcos55cos25+t^2cos25^2+sin55^2-2tsin55sin25+t^2sin25^2

=√1+t^2-2t(sin35cos25+sin25cos35)

√(1+t^2)-2tsin60

=√t^2-√3 t+1

=√[(t-√3/2)^2+1/4]

所以t=√3/2时,最小值为1/2