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# Vectors

• veczero - Returns the zero vector, {0 0 0}
```Example:
vmd > veczero
0 0 0
```

• (C++) vecadd v1 v2 [v3 ... vn] - Returns the vector sum of all the terms.
```Examples:
vmd > vecadd {1 2 3} {4 5 6} {7 8 9} {-11 -11 -11}
1 4 7
vmd > vecadd {0.1 0.2 0.4 0.8} {1 1 2 3} {3 1 4 1}
4.1 2.2 6.4 4.8
9
```

• vecmul v1 v2 - Returns the vector of a term-by-term multiply.
```Examples:
vmd > vecmul {1 2 3} {4 5 6}
4 10 18
vmd > vecmul {0.1 0.2 0.4 0.8} {1 1 2 3}
0.1 0.2 0.8 2.4
```

• (C++) vecsub v1 v2 - Returns the vector subtraction of the second term from the first
```Examples:
vmd > vecsub 6 3.2
2.8
vmd > vecsub {10 9.8 7} {0.1 0 -0.1}
9.9 9.8 7.1
vmd > vecsub {1 2 3 4 5} {6 7 8 9 10}
-5 -5 -5 -5 -5
```

• (C++) vecsum v - Returns the sum of the elements in v
```Examples:
vmd > vecsum { 1 2 3 }
6.0
```

• (C++) vecmean v - Returns the mean of the elements in v
```Examples:
vmd > vecmean { 1 2 3 }
2.0
```

• (C++) vecstddev v - Returns the standard deviation of the elements in v
```Examples:
vmd > vecstddev { 1 2 3 4 5 6 7 8 9 10 }
2.87228131294
```

• (C++) vecscale c v -
• (C++) vecscale v c - Returns the vector of the scalar value c applied to each term of v
```Examples:
vmd > vecscale .2 {1 2 3}
0.2 0.4 0.6
vmd > vecscale {-5 4 -3 2} -2
10 -8 6 -4
vmd > vecscale -2 3
-6
```

• vecdot v1 v2 - Returns the scalar dot product of the two vectors
```Examples:
vmd > vecdot {1 -2 3} {4 5 6}
12
vmd > vecdot {3 4} {3 4}
25
vmd > vecdot {1 2 3 4 5} {5 4 3 2 1}
35
vmd > vecdot 3 -2
-6
```

• veccross v1 v2 - Returns the vector cross product of the two vectors.
```Examples:
vmd > veccross {1 0 0} {0 1 0}
0 0 1
vmd > veccross {2 2 2} {-1 0 0}
0 -2 2
```

• veclength v - Returns the scalar length of v ( )
```Examples:
vmd> veclength 5
5.0
vmd > veclength {5 12}
13.0
vmd > veclength {3 4 12}
13.0
vmd > veclength {1 -2 3 -4}
5.47723
```

• veclength2 v - Returns the square of the scalar length of v ( )
```Examples:
vmd > veclength2 5
25
vmd > veclength2 {5 12}
169
vmd > veclength2 {3 4 12}
169
vmd > veclength2 {1 -2 3 -4}
30
```

• vecnorm v - Returns the vector of length 1 directed along v
```Examples:
vmd > vecnorm -10
-1.0
vmd > vecnorm {1 1 }
0.707109 0.707109
vmd > vecnorm {2 -3 1}
0.534522 -0.801783 0.267261
vmd > vecnorm {2 2 -2 2 -2 -2}
0.408248 0.408248 -0.408248 0.408248 -0.408248 -0.408248
```

• vecdist v1 v2 - Returns the distance between the two vectors ( )
```Examples:
vmd > vecdist -1.5 5.5
7.0
vmd > vecdist {0 0 0} {3 4 0}
5.0
vmd > vecdist {0 1 2 3 4 5 6} {-6 -5 -4 -3 -2 -1 0}
15.8745
```

• vecinvert v - Returns the additive inverse of v ( v).
```Examples:
vmd > vecinvert -11.1
11.1
vmd > vecinvert {3 -4 5}
-3 4 -5
vmd > vecinvert {0 -1 2 -3}
0 1 -2 3
```

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vmd@ks.uiuc.edu