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(A) Given that $\hat{a}$ and $\hat{b}$ are unit vectors, so $|\hat{a}| = 1$ and $|\hat{b}| = 1$.For $(A)$: $|\frac{\hat{a} + \hat{b}}{\sqrt{3}}| = \fr

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Only $(A), (C), (D)$

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(A) Given that $\hat{a}$ and $\hat{b}$ are unit vectors, so $|\hat{a}| = 1$ and $|\hat{b}| = 1$.For $(A)$: $|\frac{\hat{a} + \hat{b}}{\sqrt{3}}| = \frac{1}{\sqrt{3}} \sqrt{|\hat{a}|^2 + |\hat{b}|^2 + 2|\hat{a}||\hat{b}| \cos 60^{\circ}} = \frac{1}{\sqrt{3}} \sqrt{1 + 1 + 2(1)(1)(0.5)} = \frac{1}{\sqrt{3}} \sqrt{3} = 1$.For $(B)$: $|\hat{a} + \hat{b}| = \sqrt{1 + 1 + 2(1)(1)(0.5)} = \sqrt{3} 
eq 1$.For $(C)$: $|\hat{a}| = 1$.For $(D)$: $|\hat{b}| = 1$.Thus, vectors in $(A), (C),$ and $(D)$ have a magnitude of $1$.

If the angle between unit vectors $\hat{a}$ and $\hat{b}$ is $60^{\circ}$, which of the following vectors have a magnitude of $1$?
$(A)$ $\frac{\hat{a} + \hat{b}}{\sqrt{3}}$
$(B)$ $\hat{a} + \hat{b}$
$(C)$ $\hat{a}$
$(D)$ $\hat{b}$

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If the angle between unit vectors $\hat{a}$ and $\hat{b}$ is $60^{\circ}$, which of the following vectors have a magnitude of $1$?$(A)$ $\frac{\hat{a} + \hat{b}}{\sqrt{3}}$$(B)$ $\hat{a} + \hat{b}$$(C)$ $\hat{a}$$(D)$ $\hat{b}$