SICP Exercise 2.46

Question

A two-dimensional vector v running from the origin to a point can be represented as a pair consisting of an x-coordinate and a y-coordinate. Implement a data abstraction for vectors by giving a constructor make-vect and corresponding selectors xcor-vect and ycor-vect. In terms of your selectors and constructor, implement procedures add-vect, sub-vect, and scale-vect that perform the operations vector addition, vector subtraction, and multiplying a vector by a scalar:

$$(x_1,y_1)+(x_2,y_2)=(x_1+x_2,y_1+y_2)$$ $$(x_1,y_1)-(x_2,y_2)=(x_1-x_2,y_1-y_2)$$ $$s\cdot (x,y)=(sx,sy)$$

Answer

Here are the various function implementations:

copy(define (make-vect x y)
  (cons x y))

(define (xcor-vect v) (car v))

(define (ycor-vect v) (cdr v))

(define (add-vect v1 v2)
  (make-vect (+ (xcor-vect v1) (xcor-vect v2))
             (+ (ycor-vect v1) (ycor-vect v2))))

(define (sub-vect v1 v2)
  (make-vect (- (xcor-vect v1) (xcor-vect v2))
             (- (ycor-vect v1) (ycor-vect v2))))

(define (scale-vect v s)
  (make-vect (* s (xcor-vect v)) (* s (ycor-vect v))))