Sync

Task/Vector-products/00DESCRIPTION

@@ -23,7 +23,7 @@ Given the three vectors: <code>a = (3, 4, 5);  b = (4, 3, 5);  c = (-5, -12, -13
 
 ;References:
 * [[Dot product]] here on RC.
-* [http://mathworld.wolfram.com/VectorMultiplication.html A starting page] to the Wolfram Mathworld information on vector multiplication.
+* A starting page on Wolfram Mathworld is {{Wolfram|Vector|Mulitplication}}.
 * Wikipedias [[wp:Dot product|dot product]], [[wp:Cross product|cross product]] and [[wp:Triple product|triple product]] entries.
 
 ;C.f.

Task/Vector-products/Racket/vector-products.rkt

@@ -0,0 +1,30 @@
+#lang racket
+
+(define (dot-product X Y)
+  (for/sum ([x (in-vector X)] [y (in-vector Y)]) (* x y)))
+
+(define (cross-product X Y)
+  (define len (vector-length X))
+  (for/vector ([n len])
+    (define (ref V i) (vector-ref V (modulo (+ n i) len)))
+    (- (* (ref X 1) (ref Y 2)) (* (ref X 2) (ref Y 1)))))
+
+(define (scalar-triple-product X Y Z)
+  (dot-product X (cross-product Y Z)))
+
+(define (vector-triple-product X Y Z)
+  (cross-product X (cross-product Y Z)))
+
+(define A '#(3 4 5))
+(define B '#(4 3 5))
+(define C '#(-5 -12 -13))
+
+(printf "A = ~s\n" A)
+(printf "B = ~s\n" B)
+(printf "C = ~s\n" C)
+(newline)
+
+(printf "A . B = ~s\n" (dot-product A B))
+(printf "A x B = ~s\n" (cross-product A B))
+(printf "A . B x C = ~s\n" (scalar-triple-product A B C))
+(printf "A x B x C = ~s\n" (vector-triple-product A B C))