Readded vector

Vector.hs

@@ -0,0 +1,32 @@
+data Vector = V !Double !Double !Double deriving (Eq, Show)
+
+instance Num Vector where
+  (V x y z) + (V a b c) = V (x+a) (y+b) (z+c)
+  (V x y z) - (V a b c) = V (x-a) (y-b) (z-c)
+  (V x y z) * (V a b c) = V (y * c - z * b) (z * a - x * c) (x * b - y * a)
+  negate        = scale (-1)
+  abs _         = error "abs Vector not impelemented"
+  signum _      = error "signum Vector not implemented"
+  fromInteger _ = error "fromInteger Vector not impelmented"
+
+dot :: Vector -> Vector -> Double
+dot (V x y z) (V a b c) = x * a + y * b + z * c
+
+sqrMag :: Vector -> Double
+sqrMag v = v `dot` v
+
+mag :: Vector -> Double
+mag = sqrt . sqrMag
+
+projMag :: Vector -> Vector -> Double
+projMag v u = (v `dot` u) / mag u
+
+scale :: Double -> Vector -> Vector
+scale s (V x y z) = V (x*s) (y*s) (z*s)
+
+norm :: Vector -> Vector
+norm (V 0 0 0) = V 0 0 0
+norm v = scale (1 / mag v) v
+
+proj :: Vector -> Vector -> Vector
+proj v u = scale ((v `dot` u) / sqrMag u) u