Question

已知向量a=(-3,2),向量b=(2,1),向量c=(3,-1),t∈R

Answer 1

(1)通过化简,可得|a+tb|2 = 9t2 -6t + 1

=（3t-1）2,明显地,最小值为0.相应的t=1/3.

(2)两向量共线,根据共线定理,设λc=a-tb,化简得

3λ=-3-2t,-λ=2-t,进而λ=(-3-2t)/3=(2-t)/(-1),求得t=3/5