(1)设a=(x1,y1),b=(x2,y2),则有
tb=(tx2,ty2),
1/3(a+b)=(1/3(x1+x2),1/3(y1+y2)).
由于a,tb,1/3（a+b）三向量终点共线,
则:
tb-a=N(1/3(a+b)-a)
即tx2-x1=N(1/3(x1+x2)-x1)
ty2-y1=N(1/3(y1+y2)-y1)
解得 N可为2/3的倍数,t=1/2
(2)|a-tb|
=根号[(a-tb)^2]
=根号[a^2+t^2b^2-2t*a*b]
=根号[(1+t^2)b^2-2t*b^2*cos60]
=根号[(1+t^2)b^2-tb^2]
=根号[t^2-t+1]*|b|
=根号[(t-1/2)^2+3/4]*|b|
则有t=1/2时,丨a-tb丨的值最小