2.46

练习 2.46 从原点出发的一个二维向量v可以用一个由x坐标和y坐标构成的序对表示。请为这样的向量实现一个数据抽象：给出一个构造函数make-vect，以及对应的选择函数xcor-vect和ycor-vect。借助于你给出的构造函数和选择函数，实现过程add-vect、sub-vect和scale-vect，它们能完成向量加法、向量减法和向量的伸缩。

$$(x_1, y_1) + (x_2, y_2) = (x_1 + x_2, y_1 + y_2)$$

$$(x_1, y_1) - (x_2, y_2) = (x_1 - x_2, y_1 - y_2)$$

$$s\cdot(x, y) = (sx, sy)$$

 
(define make-vect cons)
(define xcor-vect car)
(define ycor-vect cdr)
​
(define v (make-vect 1 2))
v
​x
 
(1 . 2)

 
(xcor-vect v)
 
1

 
(ycor-vect v)
 
2

 
(define (add-vect v1 v2)
  (make-vect
   (+ (xcor-vect v1) (xcor-vect v2))
   (+ (ycor-vect v1) (ycor-vect v2))
   )
  )
​
(add-vect v v)
 
(2 . 4)

 
(define (sub-vect v1 v2)
  (make-vect
   (- (xcor-vect v1) (xcor-vect v2))
   (- (ycor-vect v1) (ycor-vect v2))
   )
  )
​
(sub-vect v v)
 
(0 . 0)

 
(define (scale-vect s v)
  (make-vect
   (* s (xcor-vect v))
   (* s (ycor-vect v))
   )
  )
​
(scale-vect 5 v)
 
(5 . 10)