# Concrete Abstractions: Chapter 6

Exercise 6.23
A three-dimensional (3D) vector has x, y, and z coordinates, which are numbers. 3D vectors can be constructed and accessed using the following abstract interface:

(make-3D-vector x y z)
(x-coord vector)
(y-coord vector)
(z-coord vector)

a. Using this abstract interface, define procedures for adding two vectors, finding the dot-product of two vectors, and scaling a vector by a numerical scaling factor.
b. Choose a representation for vectors and implement make-3D-vector, x-coord, y-coord, and z-coord.

Solution: a.

```(define add-vectors
(lambda (a b)
(make-3D-vector
(+ (x-coord a) (x-coord b))
(+ (y-coord a) (y-coord b))
(+ (z-coord a) (z-coord b)))))

(define dot-vectors
(lambda (a b)
(+
(* (x-coord a) (x-coord b))
(* (y-coord a) (y-coord b))
(* (z-coord a) (z-coord b)))))

(define scale-vector
(lambda (a s)
(make-3D-vector (* s (x-coord a))
(* s (y-coord a))
(* s (z-coord a)))))
```

b.

```(define make-3D-vector
(lambda (x y z)
(cons x (cons y z))))

(define x-coord
(lambda (a)
(car a)))

(define y-coord
(lambda (a)
(car (cdr a))))

(define z-coord
(lambda (a)
(cdr (cdr a))))```

This was a quite short chapter. However chapter 7 is rather long. This exercise above covers pretty much the whole chapter, it was just about cons, car and cdr.

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What can I learn?

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Conclusion

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