Question

设a,b,c为单位向量,a,b的夹角为60°,则a×c+b×c的最大值为?

Answer 1

(a+b)^2=a^2+b^2+2a*b=2+2[a][b]cos60°=2+1=3.

所以,[a+b]=√3.

a*c+b*c

=(a+b)*c

=[a+b][c]cos

=√3cos

当a+b与c共线且同向时,cos=1,(a+b)*c取得最大值为√3.