∵a,b为单位向量,∴|a|=|b|=1.
∵向量(ta-(1-t)b)⊥向量a,∴ (ta-(1-t)b).a=0.
ta^2-(1-t)b,a=0.
ta^2-ab+tab=0.
t*1-|a||b|cos120+t|a||b|cos120=0.
t-(-1/2)-(t/2)=0.
t/2+1/2=0.
∴t=-1.
|
∵a,b为单位向量,∴|a|=|b|=1.
∵向量(ta-(1-t)b)⊥向量a,∴ (ta-(1-t)b).a=0.
ta^2-(1-t)b,a=0.
ta^2-ab+tab=0.
t*1-|a||b|cos120+t|a||b|cos120=0.
t-(-1/2)-(t/2)=0.
t/2+1/2=0.
∴t=-1.
|