If the subtraction of two unit vectors is a unit vector then the angle between the first two vectors...
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Let the two vectors be (ai^+bj^+ck^) & (pi^+qj^+rk^)
Then,
(ai^+bj^+ck^) - (pi^+qj^+rk^)
= (a-p)i^ + (b-q)j^ + (c-k)k^
For this to be an unit vector, EITHER two of (a-p), (b-q) or (c-r) have to be zero. For the sake of simplicity, I take (b-q) and (c-r) to be zero.
Therefore, b=q and c=r, giving us vectors ai^+bj^+ck^ and pi^+bj^+ck^,
Therefore, angle between them is,
∆ = arc(cos[(ap + b^2 + c^2)/{√(a^2 + b^2 + c^2)√(p^2 + b^2 + c^2)}])
[NOTE : I used ∆ instead of the formal theta
arc means inverse i.e. cos inverse]
If b=c=q=r=0,
Angle ∆ = arc(cos(ap/ap))
= arc(cos 1)
= 0°
Explanation:
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