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Maybe I have developed a theory, of Vector-Vector division, which gives a scalar, just like the dot product.

Main Concept

  • vector(A)÷vector(B) = (A/B)cos(theta), where theta is the angle between the two vectors.

  • So, we can say that vector(A)÷vector(B) = (vector(A).vector(B))/B^2

Sub Concept

  • In this theory, we write can write scalar "s" in vector form as "vector(s, s, s)", this leads to the case 1÷vector(A), or s÷vector(A), which we can rewrite as s(1÷vector(A))
  • Here, vector(1, 1, 1) is called a pseudo-unit vector (represented as p cap)
  • Just as we write null vector as 0 bar, we can represent, any scalar "s" in vector quantity by just keeping an arrow on it (s bar)

If you are having any problems against the theory, or some information that may help this theory, then please give a reply and support me.

Zayaan
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  • Good thinking ! Some thoughts to take it forward : (1) You have to make it $A(B/A)=B$ & $(B/A)A=B$ , which is like the Case in rational numbers & real numbers or even matrix inverse. (2) You have to show some "usefulness" of this new Division. – Prem Nov 08 '22 at 12:33
  • What does $\mathrm{vector}(s,s,s)$ mean with three arguments? – Randall Nov 08 '22 at 13:48
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    This site is for getting answers to specific questions. I don't see a question here. – mr_e_man Nov 08 '22 at 14:30
  • @Randall vector(s, s, s) means a 3d vector with distance s in each direction – Zayaan Nov 10 '22 at 12:21

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