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(A) Given that $\hat{A}$ is a unit vector,its magnitude is constant,i.e.,$|\hat{A}| = 1$.Squaring both sides,we get $|\hat{A}|^2 = \hat{A} \cdot \hat{

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(A) Given that $\hat{A}$ is a unit vector,its magnitude is constant,i.e.,$|\hat{A}| = 1$.Squaring both sides,we get $|\hat{A}|^2 = \hat{A} \cdot \hat{A} = 1$.Differentiating both sides with respect to time $t$,we get $\frac{d}{dt}(\hat{A} \cdot \hat{A}) = \frac{d}{dt}(1)$.Using the product rule for the dot product,we have $\frac{d\hat{A}}{dt} \cdot \hat{A} + \hat{A} \cdot \frac{d\hat{A}}{dt} = 0$.Since the dot product is commutative,this simplifies to $2(\hat{A} \cdot \frac{d\hat{A}}{dt}) = 0$.Therefore,$\hat{A} \cdot \frac{d\hat{A}}{dt} = 0$.

If $\hat{A}$ is a unit vector in a given direction,then the value of $\hat{A} \cdot \frac{d\hat{A}}{dt}$ is

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