Add tasks for all the new languages

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

@@ -0,0 +1,33 @@
+import strutils
+
+type Vector3 = array[1..3, float]
+
+proc `$`(a: Vector3): string =
+  result = "["
+
+  for i, x in a:
+    if i > a.low:
+      result.add ", "
+    result.add formatFloat(x, precision = 0)
+
+  result.add "]"
+
+proc `~⨯`(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 `~•`[T](a, b: T): float =
+  for i in a.low..a.high:
+    result += a[i] * b[i]
+
+proc scalartrip(a, b, c: Vector3): float = a ~• (b ~⨯ c)
+
+proc vectortrip(a, b, c: Vector3): Vector3 = a ~⨯ (b ~⨯ 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 ~⨯ b
+echo "a • b = ", (a ~• b).formatFloat(precision = 0)
+echo "a . (b ⨯ c) = ", (scalartrip(a, b, c)).formatFloat(precision = 0)
+echo "a ⨯ (b ⨯ c) = ", vectortrip(a, b, c)