Vector
vector angle <json_vector> <json_vector2>
Description
Get the angle between two vectors (radians, in [0, pi])
Get the angle between two vectors (radians, in [0, pi])
Parameters
json_vector: A vector: JSON array of numbers, ex: [1, 2, 3] - String - required
json_vector2: A vector: JSON array of numbers - String - required
json_vector: A vector: JSON array of numbers, ex: [1, 2, 3] - String - required
json_vector2: A vector: JSON array of numbers - String - required
admin
vector angle "[1, 0, 0]" "[1, 1, 0]"
mentdb
0.7853981633974483
Orthogonal vectors: pi/2
admin
vector angle "[1, 2]" "[-2, 1]"
mentdb
1.5707963267948966
Perpendicular vectors: pi/2
admin
vector angle "[1, 0]" "[0, 1]"
mentdb
1.5707963267948966
Opposite vectors: pi
admin
vector angle "[1, 1]" "[-2, -2]"
mentdb
3.141592653589793
In degrees
admin
math rad_to_deg (vector angle "[1, 0, 0]" "[1, 1, 1]")
mentdb
54.735610317245346
vector cross <json_vector> <json_vector2>
Description
Get the cross product of two vectors of size 3
Get the cross product of two vectors of size 3
Parameters
json_vector: A vector: JSON array of numbers, ex: [1, 2, 3] - String - required
json_vector2: A vector: JSON array of numbers - String - required
json_vector: A vector: JSON array of numbers, ex: [1, 2, 3] - String - required
json_vector2: A vector: JSON array of numbers - String - required
admin
vector cross "[1, 0, 0]" "[0, 1, 0]"
mentdb
[0,0,1]
Torque r x F
admin
vector cross "[0.5, 0, 0]" "[0, 10, 0]"
mentdb
[0,0,5]
Parallel vectors: zero vector
admin
vector cross "[1, 2, 3]" "[2, 4, 6]"
mentdb
[0,0,0]
Area of the triangle (0,0,0), (1,0,0), (0,1,1): half of the norm
admin
-> "[n]" (vector norm (vector cross "[1, 0, 0]" "[0, 1, 1]")); math calc "[n]/2"
mentdb
0.7071067811865476
Not in 3 dimensions: error
admin
vector cross "[1, 2]" "[3, 4]"
mentdb
Sorry, an error appears (the cross product needs two vectors of size 3 (2 and 2)).
vector dot <json_vector> <json_vector2>
Description
Get the dot product of two vectors
Get the dot product of two vectors
Parameters
json_vector: A vector: JSON array of numbers, ex: [1, 2, 3] - String - required
json_vector2: A vector: JSON array of numbers - String - required
json_vector: A vector: JSON array of numbers, ex: [1, 2, 3] - String - required
json_vector2: A vector: JSON array of numbers - String - required
admin
vector dot "[1, 2, 3]" "[4, 5, 6]"
mentdb
32
Work of a force W = F . d
admin
vector dot "[10, 0, 5]" "[3, 4, 0]"
mentdb
30
Perpendicular: 0
admin
vector dot "[1, 2]" "[-2, 1]"
mentdb
0
Different sizes: error
admin
vector dot "[1, 2]" "[1, 2, 3]"
mentdb
Sorry, an error appears (the vectors must have the same size (2 and 3)).
vector norm <json_vector>
Description
Get the Euclidean norm of a vector
Get the Euclidean norm of a vector
Parameters
json_vector: A vector: JSON array of numbers, ex: [1, 2, 3] - String - required
json_vector: A vector: JSON array of numbers, ex: [1, 2, 3] - String - required
admin
vector norm "[3, 4]"
mentdb
5
3D vector
admin
vector norm "[1, 2, 2]"
mentdb
3
4 dimensions
admin
vector norm "[1, 1, 1, 1]"
mentdb
2
Speed from the components (m/s)
admin
vector norm "[3.2, -1.5, 0.8]"
mentdb
3.6235341863986883
vector unit <json_vector>
Description
Get the unit vector (same direction, norm 1)
Get the unit vector (same direction, norm 1)
Parameters
json_vector: A vector: JSON array of numbers, ex: [1, 2, 3] - String - required
json_vector: A vector: JSON array of numbers, ex: [1, 2, 3] - String - required
admin
vector unit "[3, 4]"
mentdb
[0.6,0.8]
3D unit vector
admin
vector unit "[1, 2, 2]"
mentdb
[0.3333333333333333,0.6666666666666666,0.6666666666666666]
Already of norm 1
admin
vector unit "[0, 1, 0]"
mentdb
[0,1,0]
Direction of a force
admin
vector unit "[10, -10, 5]"
mentdb
[0.6666666666666666,-0.6666666666666666,0.3333333333333333]
vector add <json_vector> <json_vector2>
Description
Add two vectors
Add two vectors
Parameters
json_vector: A vector: JSON array of numbers - String - required
json_vector2: A vector: JSON array of numbers - String - required
json_vector: A vector: JSON array of numbers - String - required
json_vector2: A vector: JSON array of numbers - String - required
admin
vector add "[1, 2, 3]" "[4, 5, 6]"
mentdb
[5,7,9]
Sum of two forces
admin
vector add "[3, 0]" "[0, 4]"
mentdb
[3,4]
Sum of forces
admin
vector add "[10, 0, 0]" "[0, -5, 2]"
mentdb
[10,-5,2]
Different sizes: error
admin
vector add "[1, 2]" "[1, 2, 3]"
mentdb
Sorry, an error appears (the vectors must have the same size (2 and 3)).
vector scale <json_vector> <k>
Description
Multiply a vector by a number
Multiply a vector by a number
Parameters
json_vector: A vector: JSON array of numbers - String - required
k: The number - Number - required
json_vector: A vector: JSON array of numbers - String - required
k: The number - Number - required
admin
vector scale "[1, 2, 3]" 2.5
mentdb
[2.5,5,7.5]
Opposite vector
admin
vector scale "[1, -2, 3]" -1
mentdb
[-1,2,-3]
By 0
admin
vector scale "[1, 2, 3]" 0
mentdb
[0,0,0]
Velocity x time = displacement
admin
vector scale "[2.5, 0, -1]" 4
mentdb
[10,0,-4]
vector sub <json_vector> <json_vector2>
Description
Subtract two vectors
Subtract two vectors
Parameters
json_vector: A vector: JSON array of numbers - String - required
json_vector2: A vector: JSON array of numbers - String - required
json_vector: A vector: JSON array of numbers - String - required
json_vector2: A vector: JSON array of numbers - String - required
admin
vector sub "[1, 2, 3]" "[4, 5, 6]"
mentdb
[-3,-3,-3]
Displacement between two points
admin
vector sub "[5, 7, 2]" "[1, 2, 2]"
mentdb
[4,5,0]
Vector from point A to point B: B - A
admin
vector sub "[4, 6, 1]" "[1, 2, 1]"
mentdb
[3,4,0]
Same vector: zero
admin
vector sub "[1, 2]" "[1, 2]"
mentdb
[0,0]