If the sum of two unit vectors is a unit vector, then magnitude of difference is

Question

Infinity Learn · Accepted Answer

Let $$n^1$$  and  $$n^2$$ be the two unit vectors, then the sum isn¯  $$=$$  $$n^1$$ $$+$$  $$n^2or$$ $$ns2$$  $$=$$ $$n12+n22+2n1n2cos$$θ           $$=$$ $$1+1+2cos$$θsince it is given that ns is also a unit vector, $$therefore1$$ $$=$$ $$1+1+2cos$$θ  ⇒  $$cos$$θ $$=$$ $$-12$$   ∴θ $$=$$ $$1200Now$$ the difference vector is $$n^d$$  $$=$$  $$n^1$$ −  $$n^2$$ $$ornd2$$ $$=$$ $$n12$$ $$+n22$$−$$2n1n2cos$$θ  $$=$$ $$1+1$$−$$2cos(1200)$$∴  $$nd2$$ $$=$$ $$2-2(-12)$$ $$=$$ $$2+1$$ $$=$$ $$3$$ ⇒ nd $$=$$ $$3$$

If the sum of two unit vectors is a unit vector, then magnitude of difference is

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