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(D) Given that $\hat{u}$ and $\hat{v}$ are unit vectors,so $|\hat{u}| = 1$ and $|\hat{v}| = 1$.Let $\vec{w} = 2\hat{u} 	imes 3\hat{v} = 6(\hat{u} 	i

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For exactly one value of $	heta$

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(D) Given that $\hat{u}$ and $\hat{v}$ are unit vectors,so $|\hat{u}| = 1$ and $|\hat{v}| = 1$.Let $\vec{w} = 2\hat{u} 	imes 3\hat{v} = 6(\hat{u} 	imes \hat{v})$.We are given that $\vec{w}$ is a unit vector,so $|\vec{w}| = 1$.Therefore,$|6(\hat{u} 	imes \hat{v})| = 1$.$6|\hat{u}||\hat{v}|\sin	heta = 1$,where $	heta$ is the angle between $\hat{u}$ and $\hat{v}$.Since $|\hat{u}| = 1$ and $|\hat{v}| = 1$,we have $6(1)(1)\sin	heta = 1$.$6\sin	heta = 1$,which implies $\sin	heta = \frac{1}{6}$.Since $	heta$ is an acute angle,$\sin	heta$ is positive,and there is exactly one value of $	heta$ in the interval $(0, \frac{\pi}{2})$ such that $\sin	heta = \frac{1}{6}$,which is $	heta = \arcsin(\frac{1}{6})$.Thus,there is exactly one value of $	heta$.

If $\hat{u}$ and $\hat{v}$ are unit vectors and $\theta$ is the acute angle between them,then for what value of $\theta$ is $2\hat{u} \times 3\hat{v}$ a unit vector?

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