Initial data commit

Task/Vector-products/Nim/vector-products.nim

@@ -0,0 +1,31 @@
+import strformat, strutils
+
+type Vector3 = array[1..3, float]
+
+proc `$`(a: Vector3): string =
+  result = "("
+  for x in a:
+    result.addSep(", ", 1)
+    result.add &"{x}"
+  result.add ')'
+
+proc cross(a, b: Vector3): Vector3 =
+  result = [a[2]*b[3] - a[3]*b[2], a[3]*b[1] - a[1]*b[3], a[1]*b[2] - a[2]*b[1]]
+
+proc dot(a, b: Vector3): float =
+  for i in a.low..a.high:
+    result += a[i] * b[i]
+
+proc scalarTriple(a, b, c: Vector3): float = a.dot(b.cross(c))
+
+proc vectorTriple(a, b, c: Vector3): Vector3 = a.cross(b.cross(c))
+
+let
+  a = [3.0, 4.0, 5.0]
+  b = [4.0, 3.0, 5.0]
+  c = [-5.0, -12.0, -13.0]
+
+echo &"a ⨯ b = {a.cross(b)}"
+echo &"a . b = {a.dot(b)}"
+echo &"a . (b ⨯ c) = {scalarTriple(a, b, c)}"
+echo &"a ⨯ (b ⨯ c) = {vectorTriple(a, b, c)}"