but one day you will learn to follow my way,

但总有一天你会按我的做法来
which is do the easy product,

就是做顺手的叉积
then turn the sign around.

然后翻转符号
All right. So, I don't want to spend too much time,

好了我不想花过多的时间
but let me just mention one thing because of the homework problem.

我还要说件事因为这涉及到作业的问题
Remember the dot product I said is A dot B,

记住我说过点积是 A 点乘 B
is length of A length of B cosine of the angle between them

它等于 A 的大小乘以 B 乘以 AB 夹角的余弦
But I told you another way to do A dot B,

但我说过另一种做 A 点乘 B 的方法
You get that by writing A as I times Ax plus J times Ay,

把 A 写成 I 乘以 Ax 加 J 乘以 Ay
likewise for B and taking all the different dot products

同样对 B 进行替换去掉所有不同轴的点积
when you open all the brackets,

当你把所有的括号都展开
that's where you get Ax·Bx+Ay·By.

就得到了 Ax·Bx+Ay·By