In maths, we use the symbols × and ⋅ for the same purpose. For example, ∣5×4∣=∣5⋅4∣as each of these is=20
But if you do that in vectors, like ∣∣∣a×b∣∣∣=∣∣∣a⋅b∣∣∣ then it's a Big Mistake !!!
But for some integer valued magnitudes of a and b in the range 0≤a,b≤10 and for angle θ (with some integer value in degrees, 0∘≤θ≤180∘) between them, the above said false property is observed to be true.
Find the number of ordered triples (a,b,θ).
Details and assumptions :-
∙a and b are the magnitudes of a and b respectively.
∙ For an angle θ between vectors a and b (Of course it is considered as the angle in range 0≤θ≤180∘ ), it's defined as ∣∣∣a⋅b∣∣∣=∣abcosθ∣ and ∣∣∣a×b∣∣∣=∣absinθ∣.