If the sum of two unit vectors is a unit vect | vedclass

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(B) Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that their sum $\vec{c} = \vec{a} + \vec{b}$ is also a unit vector.Given $|\vec{a}| = 1$,$|\v

Vedclass · Accepted Answer

$\sqrt{3}$

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(B) Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that their sum $\vec{c} = \vec{a} + \vec{b}$ is also a unit vector.Given $|\vec{a}| = 1$,$|\vec{b}| = 1$,and $|\vec{a} + \vec{b}| = 1$.Squaring the magnitude of the sum: $|\vec{a} + \vec{b}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + 2(\vec{a} \cdot \vec{b}) = 1^2$.Substituting the values: $1 + 1 + 2(\vec{a} \cdot \vec{b}) = 1$,which gives $2(\vec{a} \cdot \vec{b}) = -1$,so $\vec{a} \cdot \vec{b} = -1/2$.Now,the magnitude of their difference is $|\vec{a} - \vec{b}| = \sqrt{|\vec{a}|^2 + |\vec{b}|^2 - 2(\vec{a} \cdot \vec{b})}$.Substituting the values: $|\vec{a} - \vec{b}| = \sqrt{1 + 1 - 2(-1/2)} = \sqrt{1 + 1 + 1} = \sqrt{3}$.

If the sum of two unit vectors is a unit vector,what is the magnitude of their difference?

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