题目

Scientists can figure out a movie's emotional tone from the gasps(喘气) of its audience. These gases could point the way to a subtle(微妙的，精细的) form of human communication, a new study suggests.When you see a movie, you can hear the music and see the pictures. However, you don't realize here are chemical signals in the air. And they, too, could be affecting you, says Williams, who led the study. As an atmospheric chemist, he studies the chemical makeup of the air around us.Williams started out measuring the air in a soccer stadium. He noticed that levels of carbon dioxide and oth（2004•宝山区一模）已知i、j分别是与x轴、y轴正方向相同的单位向量，OB1=a•i+2j（a∈R），对任意正整数n，BnBn+1=51•i+3•2n-1j．（1）若OB1⊥B2B3，求a的值；（2）求向量OBn；（3）设向量OBn=xn•i+yn•j，求最大整数a的值，使对任意正整数n，都有xn＜yn成立．