New to Lua - Get angle between two 3D Vectors [closed] - math

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I'm trying to calculate the angle at which an object is thrown, How can I apply the formula in Lua.
I have these values:
x1,y1,z1 = 1491, 1560, 11
x2,y2,z2 = 1491, 1560, 150
I based on this video: https://www.youtube.com/watch?v=QWIZXRjMspI
I'm trying with that:
FORMULA: cos(0)=a*b/|a||b|

Answer 1

If your question is, how to write this formula in Lua, then:
Depending on your environment, you may already have some built-in data types to help out. For example, in Codea, there are predefined vec3 types and associated methods (dot, length, etc.) that help out:
local a = vec3(4, -3, 5)
local b = vec3(9, 7, -10)
local ans = math.acos(a:dot(b) / (a:len() * b:len()))
print(math.deg(ans))
If you are using pure Lua, then you could use a table to represent the 3D vectors, and write your own functions for the dot product and magnitude. The Lua math library helps in all cases:
local c = {4, -3, 5}
local d = {9, 7, -10}
local ansAgain = math.acos(myDot(c, d) / (myMag(c) * myMag(d)))
print(math.deg(ansAgain))
function myDot(a, b)
return (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3])
end
function myMag(a)
return math.sqrt((a[1] * a[1]) + (a[2] * a[2]) + (a[3] * a[3]))
end

Answer 2

Your problem can be solved using Lua's arrithmetic operators:
https://www.lua.org/manual/5.3/manual.html#3.4.1
And the functions provided by Lua's mathematical library
https://www.lua.org/manual/5.3/manual.html#6.7
All you need is some very basic Lua. Once you know a bit more you can write your own little vector library or use existing ones.