If the angle between hat{a} and hat{b} is 60^ | vedclass

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

Vedclass · Accepted Answer

Only $A, C, D$

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

If the angle between $\hat{a}$ and $\hat{b}$ is $60^{\circ}$,then which of the following vector$(s)$ have magnitude one?

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